Evaluation of Kurtosis into the product of two normally distributed variables

NASA Astrophysics Data System (ADS)

Oliveira, Amílcar; Oliveira, Teresa; Seijas-Macías, Antonio

2016-06-01

Kurtosis (κ) is any measure of the "peakedness" of a distribution of a real-valued random variable. We study the evolution of the Kurtosis for the product of two normally distributed variables. Product of two normal variables is a very common problem for some areas of study, like, physics, economics, psychology, … Normal variables have a constant value for kurtosis (κ = 3), independently of the value of the two parameters: mean and variance. In fact, the excess kurtosis is defined as κ- 3 and the Normal Distribution Kurtosis is zero. The product of two normally distributed variables is a function of the parameters of the two variables and the correlation between then, and the range for kurtosis is in [0, 6] for independent variables and in [0, 12] when correlation between then is allowed.

Distribution Functions of Sizes and Fluxes Determined from Supra-Arcade Downflows

NASA Technical Reports Server (NTRS)

McKenzie, D.; Savage, S.

2011-01-01

The frequency distributions of sizes and fluxes of supra-arcade downflows (SADs) provide information about the process of their creation. For example, a fractal creation process may be expected to yield a power-law distribution of sizes and/or fluxes. We examine 120 cross-sectional areas and magnetic flux estimates found by Savage & McKenzie for SADs, and find that (1) the areas are consistent with a log-normal distribution and (2) the fluxes are consistent with both a log-normal and an exponential distribution. Neither set of measurements is compatible with a power-law distribution nor a normal distribution. As a demonstration of the applicability of these findings to improved understanding of reconnection, we consider a simple SAD growth scenario with minimal assumptions, capable of producing a log-normal distribution.

Estimating Non-Normal Latent Trait Distributions within Item Response Theory Using True and Estimated Item Parameters

ERIC Educational Resources Information Center

Sass, D. A.; Schmitt, T. A.; Walker, C. M.

2008-01-01

Item response theory (IRT) procedures have been used extensively to study normal latent trait distributions and have been shown to perform well; however, less is known concerning the performance of IRT with non-normal latent trait distributions. This study investigated the degree of latent trait estimation error under normal and non-normal…

Quantiles for Finite Mixtures of Normal Distributions

ERIC Educational Resources Information Center

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions

PubMed Central

Abanto-Valle, C. A.; Bandyopadhyay, D.; Lachos, V. H.; Enriquez, I.

2009-01-01

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of- sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model. PMID:20730043

Log Normal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of Alpha Particle Track Autoradiography

PubMed Central

Neti, Prasad V.S.V.; Howell, Roger W.

2008-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log normal distribution function (J Nucl Med 47, 6 (2006) 1049-1058) with the aid of an autoradiographic approach. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analyses of these data. Methods The measured distributions of alpha particle tracks per cell were subjected to statistical tests with Poisson (P), log normal (LN), and Poisson – log normal (P – LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL 210Po-citrate. When cells were exposed to 67 kBq/mL, the P – LN distribution function gave a better fit, however, the underlying activity distribution remained log normal. Conclusions The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:16741316

Mapping of quantitative trait loci using the skew-normal distribution.

PubMed

Fernandes, Elisabete; Pacheco, António; Penha-Gonçalves, Carlos

2007-11-01

In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use the previous model after data transformation. However, an appropriate transformation may not exist or may be difficult to find. Also this approach can raise interpretation issues. An interesting alternative is to consider a skew-normal mixture model in standard IM, and the resulting method is here denoted as skew-normal IM. This flexible model that includes the usual symmetric normal distribution as a special case is important, allowing continuous variation from normality to non-normality. In this paper we briefly introduce the main peculiarities of the skew-normal distribution. The maximum likelihood estimates of parameters of the skew-normal distribution are obtained by the expectation-maximization (EM) algorithm. The proposed model is illustrated with real data from an intercross experiment that shows a significant departure from the normality assumption. The performance of the skew-normal IM is assessed via stochastic simulation. The results indicate that the skew-normal IM has higher power for QTL detection and better precision of QTL location as compared to standard IM and nonparametric IM.

On the generation of log-Lévy distributions and extreme randomness

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2011-10-01

The log-normal distribution is prevalent across the sciences, as it emerges from the combination of multiplicative processes and the central limit theorem (CLT). The CLT, beyond yielding the normal distribution, also yields the class of Lévy distributions. The log-Lévy distributions are the Lévy counterparts of the log-normal distribution, they appear in the context of ultraslow diffusion processes, and they are categorized by Mandelbrot as belonging to the class of extreme randomness. In this paper, we present a natural stochastic growth model from which both the log-normal distribution and the log-Lévy distributions emerge universally—the former in the case of deterministic underlying setting, and the latter in the case of stochastic underlying setting. In particular, we establish a stochastic growth model which universally generates Mandelbrot’s extreme randomness.

Optimal transformations leading to normal distributions of positron emission tomography standardized uptake values.

PubMed

Scarpelli, Matthew; Eickhoff, Jens; Cuna, Enrique; Perlman, Scott; Jeraj, Robert

2018-01-30

The statistical analysis of positron emission tomography (PET) standardized uptake value (SUV) measurements is challenging due to the skewed nature of SUV distributions. This limits utilization of powerful parametric statistical models for analyzing SUV measurements. An ad-hoc approach, which is frequently used in practice, is to blindly use a log transformation, which may or may not result in normal SUV distributions. This study sought to identify optimal transformations leading to normally distributed PET SUVs extracted from tumors and assess the effects of therapy on the optimal transformations. The optimal transformation for producing normal distributions of tumor SUVs was identified by iterating the Box-Cox transformation parameter (λ) and selecting the parameter that maximized the Shapiro-Wilk P-value. Optimal transformations were identified for tumor SUV max distributions at both pre and post treatment. This study included 57 patients that underwent 18 F-fluorodeoxyglucose ( 18 F-FDG) PET scans (publically available dataset). In addition, to test the generality of our transformation methodology, we included analysis of 27 patients that underwent 18 F-Fluorothymidine ( 18 F-FLT) PET scans at our institution. After applying the optimal Box-Cox transformations, neither the pre nor the post treatment 18 F-FDG SUV distributions deviated significantly from normality (P  >  0.10). Similar results were found for 18 F-FLT PET SUV distributions (P  >  0.10). For both 18 F-FDG and 18 F-FLT SUV distributions, the skewness and kurtosis increased from pre to post treatment, leading to a decrease in the optimal Box-Cox transformation parameter from pre to post treatment. There were types of distributions encountered for both 18 F-FDG and 18 F-FLT where a log transformation was not optimal for providing normal SUV distributions. Optimization of the Box-Cox transformation, offers a solution for identifying normal SUV transformations for when the log transformation is insufficient. The log transformation is not always the appropriate transformation for producing normally distributed PET SUVs.

Optimal transformations leading to normal distributions of positron emission tomography standardized uptake values

NASA Astrophysics Data System (ADS)

Scarpelli, Matthew; Eickhoff, Jens; Cuna, Enrique; Perlman, Scott; Jeraj, Robert

2018-02-01

The statistical analysis of positron emission tomography (PET) standardized uptake value (SUV) measurements is challenging due to the skewed nature of SUV distributions. This limits utilization of powerful parametric statistical models for analyzing SUV measurements. An ad-hoc approach, which is frequently used in practice, is to blindly use a log transformation, which may or may not result in normal SUV distributions. This study sought to identify optimal transformations leading to normally distributed PET SUVs extracted from tumors and assess the effects of therapy on the optimal transformations. Methods. The optimal transformation for producing normal distributions of tumor SUVs was identified by iterating the Box-Cox transformation parameter (λ) and selecting the parameter that maximized the Shapiro-Wilk P-value. Optimal transformations were identified for tumor SUVmax distributions at both pre and post treatment. This study included 57 patients that underwent 18F-fluorodeoxyglucose (18F-FDG) PET scans (publically available dataset). In addition, to test the generality of our transformation methodology, we included analysis of 27 patients that underwent 18F-Fluorothymidine (18F-FLT) PET scans at our institution. Results. After applying the optimal Box-Cox transformations, neither the pre nor the post treatment 18F-FDG SUV distributions deviated significantly from normality (P  >  0.10). Similar results were found for 18F-FLT PET SUV distributions (P  >  0.10). For both 18F-FDG and 18F-FLT SUV distributions, the skewness and kurtosis increased from pre to post treatment, leading to a decrease in the optimal Box-Cox transformation parameter from pre to post treatment. There were types of distributions encountered for both 18F-FDG and 18F-FLT where a log transformation was not optimal for providing normal SUV distributions. Conclusion. Optimization of the Box-Cox transformation, offers a solution for identifying normal SUV transformations for when the log transformation is insufficient. The log transformation is not always the appropriate transformation for producing normally distributed PET SUVs.

Study on probability distribution of prices in electricity market: A case study of zhejiang province, china

NASA Astrophysics Data System (ADS)

Zhou, H.; Chen, B.; Han, Z. X.; Zhang, F. Q.

2009-05-01

The study on probability density function and distribution function of electricity prices contributes to the power suppliers and purchasers to estimate their own management accurately, and helps the regulator monitor the periods deviating from normal distribution. Based on the assumption of normal distribution load and non-linear characteristic of the aggregate supply curve, this paper has derived the distribution of electricity prices as the function of random variable of load. The conclusion has been validated with the electricity price data of Zhejiang market. The results show that electricity prices obey normal distribution approximately only when supply-demand relationship is loose, whereas the prices deviate from normal distribution and present strong right-skewness characteristic. Finally, the real electricity markets also display the narrow-peak characteristic when undersupply occurs.

A closer look at the effect of preliminary goodness-of-fit testing for normality for the one-sample t-test.

PubMed

Rochon, Justine; Kieser, Meinhard

2011-11-01

Student's one-sample t-test is a commonly used method when inference about the population mean is made. As advocated in textbooks and articles, the assumption of normality is often checked by a preliminary goodness-of-fit (GOF) test. In a paper recently published by Schucany and Ng it was shown that, for the uniform distribution, screening of samples by a pretest for normality leads to a more conservative conditional Type I error rate than application of the one-sample t-test without preliminary GOF test. In contrast, for the exponential distribution, the conditional level is even more elevated than the Type I error rate of the t-test without pretest. We examine the reasons behind these characteristics. In a simulation study, samples drawn from the exponential, lognormal, uniform, Student's t-distribution with 2 degrees of freedom (t(2) ) and the standard normal distribution that had passed normality screening, as well as the ingredients of the test statistics calculated from these samples, are investigated. For non-normal distributions, we found that preliminary testing for normality may change the distribution of means and standard deviations of the selected samples as well as the correlation between them (if the underlying distribution is non-symmetric), thus leading to altered distributions of the resulting test statistics. It is shown that for skewed distributions the excess in Type I error rate may be even more pronounced when testing one-sided hypotheses. ©2010 The British Psychological Society.

Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability.

PubMed

van Albada, S J; Robinson, P A

2007-04-15

Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, these methods do not always give good agreement with the Gaussian. A transformation is discussed that maps probability distributions as closely as possible to the normal distribution, with exact agreement for continuous distributions. To illustrate, the transformation is applied to a theoretical distribution, and to quantitative electroencephalographic (qEEG) measures from repeat recordings of 32 subjects which are highly non-normal. Agreement with the Gaussian was better than using logarithmic, logit, or Box-Cox transformations. Since normal data have previously been shown to have better test-retest reliability than non-normal data under fairly general circumstances, the implications of our transformation for the test-retest reliability of parameters were investigated. Reliability was shown to improve with the transformation, where the improvement was comparable to that using Box-Cox. An advantage of the general transformation is that it does not require laborious optimization over a range of parameters or a case-specific choice of form.

Dichotomisation using a distributional approach when the outcome is skewed.

PubMed

Sauzet, Odile; Ofuya, Mercy; Peacock, Janet L

2015-04-24

Dichotomisation of continuous outcomes has been rightly criticised by statisticians because of the loss of information incurred. However to communicate a comparison of risks, dichotomised outcomes may be necessary. Peacock et al. developed a distributional approach to the dichotomisation of normally distributed outcomes allowing the presentation of a comparison of proportions with a measure of precision which reflects the comparison of means. Many common health outcomes are skewed so that the distributional method for the dichotomisation of continuous outcomes may not apply. We present a methodology to obtain dichotomised outcomes for skewed variables illustrated with data from several observational studies. We also report the results of a simulation study which tests the robustness of the method to deviation from normality and assess the validity of the newly developed method. The review showed that the pattern of dichotomisation was varying between outcomes. Birthweight, Blood pressure and BMI can either be transformed to normal so that normal distributional estimates for a comparison of proportions can be obtained or better, the skew-normal method can be used. For gestational age, no satisfactory transformation is available and only the skew-normal method is reliable. The normal distributional method is reliable also when there are small deviations from normality. The distributional method with its applicability for common skewed data allows researchers to provide both continuous and dichotomised estimates without losing information or precision. This will have the effect of providing a practical understanding of the difference in means in terms of proportions.

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

PubMed

Levine, M W

1991-01-01

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

New spatial upscaling methods for multi-point measurements: From normal to p-normal

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Xin

2017-12-01

Careful attention must be given to determining whether the geophysical variables of interest are normally distributed, since the assumption of a normal distribution may not accurately reflect the probability distribution of some variables. As a generalization of the normal distribution, the p-normal distribution and its corresponding maximum likelihood estimation (the least power estimation, LPE) were introduced in upscaling methods for multi-point measurements. Six methods, including three normal-based methods, i.e., arithmetic average, least square estimation, block kriging, and three p-normal-based methods, i.e., LPE, geostatistics LPE and inverse distance weighted LPE are compared in two types of experiments: a synthetic experiment to evaluate the performance of the upscaling methods in terms of accuracy, stability and robustness, and a real-world experiment to produce real-world upscaling estimates using soil moisture data obtained from multi-scale observations. The results show that the p-normal-based methods produced lower mean absolute errors and outperformed the other techniques due to their universality and robustness. We conclude that introducing appropriate statistical parameters into an upscaling strategy can substantially improve the estimation, especially if the raw measurements are disorganized; however, further investigation is required to determine which parameter is the most effective among variance, spatial correlation information and parameter p.

Is Coefficient Alpha Robust to Non-Normal Data?

PubMed Central

Sheng, Yanyan; Sheng, Zhaohui

2011-01-01

Coefficient alpha has been a widely used measure by which internal consistency reliability is assessed. In addition to essential tau-equivalence and uncorrelated errors, normality has been noted as another important assumption for alpha. Earlier work on evaluating this assumption considered either exclusively non-normal error score distributions, or limited conditions. In view of this and the availability of advanced methods for generating univariate non-normal data, Monte Carlo simulations were conducted to show that non-normal distributions for true or error scores do create problems for using alpha to estimate the internal consistency reliability. The sample coefficient alpha is affected by leptokurtic true score distributions, or skewed and/or kurtotic error score distributions. Increased sample sizes, not test lengths, help improve the accuracy, bias, or precision of using it with non-normal data. PMID:22363306

A random effects meta-analysis model with Box-Cox transformation.

PubMed

Yamaguchi, Yusuke; Maruo, Kazushi; Partlett, Christopher; Riley, Richard D

2017-07-19

In a random effects meta-analysis model, true treatment effects for each study are routinely assumed to follow a normal distribution. However, normality is a restrictive assumption and the misspecification of the random effects distribution may result in a misleading estimate of overall mean for the treatment effect, an inappropriate quantification of heterogeneity across studies and a wrongly symmetric prediction interval. We focus on problems caused by an inappropriate normality assumption of the random effects distribution, and propose a novel random effects meta-analysis model where a Box-Cox transformation is applied to the observed treatment effect estimates. The proposed model aims to normalise an overall distribution of observed treatment effect estimates, which is sum of the within-study sampling distributions and the random effects distribution. When sampling distributions are approximately normal, non-normality in the overall distribution will be mainly due to the random effects distribution, especially when the between-study variation is large relative to the within-study variation. The Box-Cox transformation addresses this flexibly according to the observed departure from normality. We use a Bayesian approach for estimating parameters in the proposed model, and suggest summarising the meta-analysis results by an overall median, an interquartile range and a prediction interval. The model can be applied for any kind of variables once the treatment effect estimate is defined from the variable. A simulation study suggested that when the overall distribution of treatment effect estimates are skewed, the overall mean and conventional I 2 from the normal random effects model could be inappropriate summaries, and the proposed model helped reduce this issue. We illustrated the proposed model using two examples, which revealed some important differences on summary results, heterogeneity measures and prediction intervals from the normal random effects model. The random effects meta-analysis with the Box-Cox transformation may be an important tool for examining robustness of traditional meta-analysis results against skewness on the observed treatment effect estimates. Further critical evaluation of the method is needed.

On Nonequivalence of Several Procedures of Structural Equation Modeling

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Chan, Wai

2005-01-01

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…

Robustness of location estimators under t-distributions: a literature review

NASA Astrophysics Data System (ADS)

Sumarni, C.; Sadik, K.; Notodiputro, K. A.; Sartono, B.

2017-03-01

The assumption of normality is commonly used in estimation of parameters in statistical modelling, but this assumption is very sensitive to outliers. The t-distribution is more robust than the normal distribution since the t-distributions have longer tails. The robustness measures of location estimators under t-distributions are reviewed and discussed in this paper. For the purpose of illustration we use the onion yield data which includes outliers as a case study and showed that the t model produces better fit than the normal model.

A short note on the maximal point-biserial correlation under non-normality.

PubMed

Cheng, Ying; Liu, Haiyan

2016-11-01

The aim of this paper is to derive the maximal point-biserial correlation under non-normality. Several widely used non-normal distributions are considered, namely the uniform distribution, t-distribution, exponential distribution, and a mixture of two normal distributions. Results show that the maximal point-biserial correlation, depending on the non-normal continuous variable underlying the binary manifest variable, may not be a function of p (the probability that the dichotomous variable takes the value 1), can be symmetric or non-symmetric around p = .5, and may still lie in the range from -1.0 to 1.0. Therefore researchers should exercise caution when they interpret their sample point-biserial correlation coefficients based on popular beliefs that the maximal point-biserial correlation is always smaller than 1, and that the size of the correlation is always further restricted as p deviates from .5. © 2016 The British Psychological Society.

Empirical analysis on the runners' velocity distribution in city marathons

NASA Astrophysics Data System (ADS)

Lin, Zhenquan; Meng, Fan

2018-01-01

In recent decades, much researches have been performed on human temporal activity and mobility patterns, while few investigations have been made to examine the features of the velocity distributions of human mobility patterns. In this paper, we investigated empirically the velocity distributions of finishers in New York City marathon, American Chicago marathon, Berlin marathon and London marathon. By statistical analyses on the datasets of the finish time records, we captured some statistical features of human behaviors in marathons: (1) The velocity distributions of all finishers and of partial finishers in the fastest age group both follow log-normal distribution; (2) In the New York City marathon, the velocity distribution of all male runners in eight 5-kilometer internal timing courses undergoes two transitions: from log-normal distribution at the initial stage (several initial courses) to the Gaussian distribution at the middle stage (several middle courses), and to log-normal distribution at the last stage (several last courses); (3) The intensity of the competition, which is described by the root-mean-square value of the rank changes of all runners, goes weaker from initial stage to the middle stage corresponding to the transition of the velocity distribution from log-normal distribution to Gaussian distribution, and when the competition gets stronger in the last course of the middle stage, there will come a transition from Gaussian distribution to log-normal one at last stage. This study may enrich the researches on human mobility patterns and attract attentions on the velocity features of human mobility.

Notes on power of normality tests of error terms in regression models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Střelec, Luboš

2015-03-10

Normality is one of the basic assumptions in applying statistical procedures. For example in linear regression most of the inferential procedures are based on the assumption of normality, i.e. the disturbance vector is assumed to be normally distributed. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Thus, error terms should be normally distributed in order to allow us to make exact inferences. As a consequence, normally distributed stochastic errors are necessary in order to make a not misleading inferences which explains a necessity and importancemore » of robust tests of normality. Therefore, the aim of this contribution is to discuss normality testing of error terms in regression models. In this contribution, we introduce the general RT class of robust tests for normality, and present and discuss the trade-off between power and robustness of selected classical and robust normality tests of error terms in regression models.« less

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

Normalization of High Dimensional Genomics Data Where the Distribution of the Altered Variables Is Skewed

PubMed Central

Landfors, Mattias; Philip, Philge; Rydén, Patrik; Stenberg, Per

2011-01-01

Genome-wide analysis of gene expression or protein binding patterns using different array or sequencing based technologies is now routinely performed to compare different populations, such as treatment and reference groups. It is often necessary to normalize the data obtained to remove technical variation introduced in the course of conducting experimental work, but standard normalization techniques are not capable of eliminating technical bias in cases where the distribution of the truly altered variables is skewed, i.e. when a large fraction of the variables are either positively or negatively affected by the treatment. However, several experiments are likely to generate such skewed distributions, including ChIP-chip experiments for the study of chromatin, gene expression experiments for the study of apoptosis, and SNP-studies of copy number variation in normal and tumour tissues. A preliminary study using spike-in array data established that the capacity of an experiment to identify altered variables and generate unbiased estimates of the fold change decreases as the fraction of altered variables and the skewness increases. We propose the following work-flow for analyzing high-dimensional experiments with regions of altered variables: (1) Pre-process raw data using one of the standard normalization techniques. (2) Investigate if the distribution of the altered variables is skewed. (3) If the distribution is not believed to be skewed, no additional normalization is needed. Otherwise, re-normalize the data using a novel HMM-assisted normalization procedure. (4) Perform downstream analysis. Here, ChIP-chip data and simulated data were used to evaluate the performance of the work-flow. It was found that skewed distributions can be detected by using the novel DSE-test (Detection of Skewed Experiments). Furthermore, applying the HMM-assisted normalization to experiments where the distribution of the truly altered variables is skewed results in considerably higher sensitivity and lower bias than can be attained using standard and invariant normalization methods. PMID:22132175

Approximations to the distribution of a test statistic in covariance structure analysis: A comprehensive study.

PubMed

Wu, Hao

2018-05-01

In structural equation modelling (SEM), a robust adjustment to the test statistic or to its reference distribution is needed when its null distribution deviates from a χ 2 distribution, which usually arises when data do not follow a multivariate normal distribution. Unfortunately, existing studies on this issue typically focus on only a few methods and neglect the majority of alternative methods in statistics. Existing simulation studies typically consider only non-normal distributions of data that either satisfy asymptotic robustness or lead to an asymptotic scaled χ 2 distribution. In this work we conduct a comprehensive study that involves both typical methods in SEM and less well-known methods from the statistics literature. We also propose the use of several novel non-normal data distributions that are qualitatively different from the non-normal distributions widely used in existing studies. We found that several under-studied methods give the best performance under specific conditions, but the Satorra-Bentler method remains the most viable method for most situations. © 2017 The British Psychological Society.

Non-normal Distributions Commonly Used in Health, Education, and Social Sciences: A Systematic Review

PubMed Central

Bono, Roser; Blanca, María J.; Arnau, Jaume; Gómez-Benito, Juana

2017-01-01

Statistical analysis is crucial for research and the choice of analytical technique should take into account the specific distribution of data. Although the data obtained from health, educational, and social sciences research are often not normally distributed, there are very few studies detailing which distributions are most likely to represent data in these disciplines. The aim of this systematic review was to determine the frequency of appearance of the most common non-normal distributions in the health, educational, and social sciences. The search was carried out in the Web of Science database, from which we retrieved the abstracts of papers published between 2010 and 2015. The selection was made on the basis of the title and the abstract, and was performed independently by two reviewers. The inter-rater reliability for article selection was high (Cohen’s kappa = 0.84), and agreement regarding the type of distribution reached 96.5%. A total of 262 abstracts were included in the final review. The distribution of the response variable was reported in 231 of these abstracts, while in the remaining 31 it was merely stated that the distribution was non-normal. In terms of their frequency of appearance, the most-common non-normal distributions can be ranked in descending order as follows: gamma, negative binomial, multinomial, binomial, lognormal, and exponential. In addition to identifying the distributions most commonly used in empirical studies these results will help researchers to decide which distributions should be included in simulation studies examining statistical procedures. PMID:28959227

Log-Normal Distribution of Cosmic Voids in Simulations and Mocks

NASA Astrophysics Data System (ADS)

Russell, E.; Pycke, J.-R.

2017-01-01

Following up on previous studies, we complete here a full analysis of the void size distributions of the Cosmic Void Catalog based on three different simulation and mock catalogs: dark matter (DM), haloes, and galaxies. Based on this analysis, we attempt to answer two questions: Is a three-parameter log-normal distribution a good candidate to satisfy the void size distributions obtained from different types of environments? Is there a direct relation between the shape parameters of the void size distribution and the environmental effects? In an attempt to answer these questions, we find here that all void size distributions of these data samples satisfy the three-parameter log-normal distribution whether the environment is dominated by DM, haloes, or galaxies. In addition, the shape parameters of the three-parameter log-normal void size distribution seem highly affected by environment, particularly existing substructures. Therefore, we show two quantitative relations given by linear equations between the skewness and the maximum tree depth, and between the variance of the void size distribution and the maximum tree depth, directly from the simulated data. In addition to this, we find that the percentage of voids with nonzero central density in the data sets has a critical importance. If the number of voids with nonzero central density reaches ≥3.84% in a simulation/mock sample, then a second population is observed in the void size distributions. This second population emerges as a second peak in the log-normal void size distribution at larger radius.

SENSITIVITY OF NORMAL THEORY METHODS TO MODEL MISSPECIFICATION IN THE CALCULATION OF UPPER CONFIDENCE LIMITS ON THE RISK FUNCTION FOR CONTINUOUS RESPONSES. (R825385)

EPA Science Inventory

Normal theory procedures for calculating upper confidence limits (UCL) on the risk function for continuous responses work well when the data come from a normal distribution. However, if the data come from an alternative distribution, the application of the normal theory procedure...

Log-normal distribution of the trace element data results from a mixture of stocahstic input and deterministic internal dynamics.

PubMed

Usuda, Kan; Kono, Koichi; Dote, Tomotaro; Shimizu, Hiroyasu; Tominaga, Mika; Koizumi, Chisato; Nakase, Emiko; Toshina, Yumi; Iwai, Junko; Kawasaki, Takashi; Akashi, Mitsuya

2002-04-01

In previous article, we showed a log-normal distribution of boron and lithium in human urine. This type of distribution is common in both biological and nonbiological applications. It can be observed when the effects of many independent variables are combined, each of which having any underlying distribution. Although elemental excretion depends on many variables, the one-compartment open model following a first-order process can be used to explain the elimination of elements. The rate of excretion is proportional to the amount present of any given element; that is, the same percentage of an existing element is eliminated per unit time, and the element concentration is represented by a deterministic negative power function of time in the elimination time-course. Sampling is of a stochastic nature, so the dataset of time variables in the elimination phase when the sample was obtained is expected to show Normal distribution. The time variable appears as an exponent of the power function, so a concentration histogram is that of an exponential transformation of Normally distributed time. This is the reason why the element concentration shows a log-normal distribution. The distribution is determined not by the element concentration itself, but by the time variable that defines the pharmacokinetic equation.

Descriptive Statistics for Modern Test Score Distributions: Skewness, Kurtosis, Discreteness, and Ceiling Effects.

PubMed

Ho, Andrew D; Yu, Carol C

2015-06-01

Many statistical analyses benefit from the assumption that unconditional or conditional distributions are continuous and normal. More than 50 years ago in this journal, Lord and Cook chronicled departures from normality in educational tests, and Micerri similarly showed that the normality assumption is met rarely in educational and psychological practice. In this article, the authors extend these previous analyses to state-level educational test score distributions that are an increasingly common target of high-stakes analysis and interpretation. Among 504 scale-score and raw-score distributions from state testing programs from recent years, nonnormal distributions are common and are often associated with particular state programs. The authors explain how scaling procedures from item response theory lead to nonnormal distributions as well as unusual patterns of discreteness. The authors recommend that distributional descriptive statistics be calculated routinely to inform model selection for large-scale test score data, and they illustrate consequences of nonnormality using sensitivity studies that compare baseline results to those from normalized score scales.

WE-H-207A-03: The Universality of the Lognormal Behavior of [F-18]FLT PET SUV Measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scarpelli, M; Eickhoff, J; Perlman, S

Purpose: Log transforming [F-18]FDG PET standardized uptake values (SUVs) has been shown to lead to normal SUV distributions, which allows utilization of powerful parametric statistical models. This study identified the optimal transformation leading to normally distributed [F-18]FLT PET SUVs from solid tumors and offers an example of how normal distributions permits analysis of non-independent/correlated measurements. Methods: Forty patients with various metastatic diseases underwent up to six FLT PET/CT scans during treatment. Tumors were identified by nuclear medicine physician and manually segmented. Average uptake was extracted for each patient giving a global SUVmean (gSUVmean) for each scan. The Shapiro-Wilk test wasmore » used to test distribution normality. One parameter Box-Cox transformations were applied to each of the six gSUVmean distributions and the optimal transformation was found by selecting the parameter that maximized the Shapiro-Wilk test statistic. The relationship between gSUVmean and a serum biomarker (VEGF) collected at imaging timepoints was determined using a linear mixed effects model (LMEM), which accounted for correlated/non-independent measurements from the same individual. Results: Untransformed gSUVmean distributions were found to be significantly non-normal (p<0.05). The optimal transformation parameter had a value of 0.3 (95%CI: −0.4 to 1.6). Given the optimal parameter was close to zero (which corresponds to log transformation), the data were subsequently log transformed. All log transformed gSUVmean distributions were normally distributed (p>0.10 for all timepoints). Log transformed data were incorporated into the LMEM. VEGF serum levels significantly correlated with gSUVmean (p<0.001), revealing log-linear relationship between SUVs and underlying biology. Conclusion: Failure to account for correlated/non-independent measurements can lead to invalid conclusions and motivated transformation to normally distributed SUVs. The log transformation was found to be close to optimal and sufficient for obtaining normally distributed FLT PET SUVs. These transformations allow utilization of powerful LMEMs when analyzing quantitative imaging metrics.« less

Non-Gaussian Distributions Affect Identification of Expression Patterns, Functional Annotation, and Prospective Classification in Human Cancer Genomes

PubMed Central

Marko, Nicholas F.; Weil, Robert J.

2012-01-01

Introduction Gene expression data is often assumed to be normally-distributed, but this assumption has not been tested rigorously. We investigate the distribution of expression data in human cancer genomes and study the implications of deviations from the normal distribution for translational molecular oncology research. Methods We conducted a central moments analysis of five cancer genomes and performed empiric distribution fitting to examine the true distribution of expression data both on the complete-experiment and on the individual-gene levels. We used a variety of parametric and nonparametric methods to test the effects of deviations from normality on gene calling, functional annotation, and prospective molecular classification using a sixth cancer genome. Results Central moments analyses reveal statistically-significant deviations from normality in all of the analyzed cancer genomes. We observe as much as 37% variability in gene calling, 39% variability in functional annotation, and 30% variability in prospective, molecular tumor subclassification associated with this effect. Conclusions Cancer gene expression profiles are not normally-distributed, either on the complete-experiment or on the individual-gene level. Instead, they exhibit complex, heavy-tailed distributions characterized by statistically-significant skewness and kurtosis. The non-Gaussian distribution of this data affects identification of differentially-expressed genes, functional annotation, and prospective molecular classification. These effects may be reduced in some circumstances, although not completely eliminated, by using nonparametric analytics. This analysis highlights two unreliable assumptions of translational cancer gene expression analysis: that “small” departures from normality in the expression data distributions are analytically-insignificant and that “robust” gene-calling algorithms can fully compensate for these effects. PMID:23118863

A quantitative trait locus mixture model that avoids spurious LOD score peaks.

PubMed Central

Feenstra, Bjarke; Skovgaard, Ib M

2004-01-01

In standard interval mapping of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. At any given location in the genome, the evidence of a putative QTL is measured by the likelihood ratio of the mixture model compared to a single normal distribution (the LOD score). This approach can occasionally produce spurious LOD score peaks in regions of low genotype information (e.g., widely spaced markers), especially if the phenotype distribution deviates markedly from a normal distribution. Such peaks are not indicative of a QTL effect; rather, they are caused by the fact that a mixture of normals always produces a better fit than a single normal distribution. In this study, a mixture model for QTL mapping that avoids the problems of such spurious LOD score peaks is presented. PMID:15238544

A quantitative trait locus mixture model that avoids spurious LOD score peaks.

PubMed

Feenstra, Bjarke; Skovgaard, Ib M

2004-06-01

In standard interval mapping of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. At any given location in the genome, the evidence of a putative QTL is measured by the likelihood ratio of the mixture model compared to a single normal distribution (the LOD score). This approach can occasionally produce spurious LOD score peaks in regions of low genotype information (e.g., widely spaced markers), especially if the phenotype distribution deviates markedly from a normal distribution. Such peaks are not indicative of a QTL effect; rather, they are caused by the fact that a mixture of normals always produces a better fit than a single normal distribution. In this study, a mixture model for QTL mapping that avoids the problems of such spurious LOD score peaks is presented.

Estimating sales and sales market share from sales rank data for consumer appliances

NASA Astrophysics Data System (ADS)

Touzani, Samir; Van Buskirk, Robert

2016-06-01

Our motivation in this work is to find an adequate probability distribution to fit sales volumes of different appliances. This distribution allows for the translation of sales rank into sales volume. This paper shows that the log-normal distribution and specifically the truncated version are well suited for this purpose. We demonstrate that using sales proxies derived from a calibrated truncated log-normal distribution function can be used to produce realistic estimates of market average product prices, and product attributes. We show that the market averages calculated with the sales proxies derived from the calibrated, truncated log-normal distribution provide better market average estimates than sales proxies estimated with simpler distribution functions.

Analysis of vector wind change with respect to time for Cape Kennedy, Florida: Wind aloft profile change vs. time, phase 1

NASA Technical Reports Server (NTRS)

Adelfang, S. I.

1977-01-01

Wind vector change with respect to time at Cape Kennedy, Florida, is examined according to the theory of multivariate normality. The joint distribution of the four variables represented by the components of the wind vector at an initial time and after a specified elapsed time is hypothesized to be quadravariate normal; the fourteen statistics of this distribution, calculated from fifteen years of twice daily Rawinsonde data are presented by monthly reference periods for each month from 0 to 27 km. The hypotheses that the wind component changes with respect to time is univariate normal, the joint distribution of wind component changes is bivariate normal, and the modulus of vector wind change is Rayleigh, has been tested by comparison with observed distributions. Statistics of the conditional bivariate normal distributions of vector wind at a future time given the vector wind at an initial time are derived. Wind changes over time periods from one to five hours, calculated from Jimsphere data, are presented.

The law of distribution of light beam direction fluctuations in telescopes. [normal density functions

NASA Technical Reports Server (NTRS)

Divinskiy, M. L.; Kolchinskiy, I. G.

1974-01-01

The distribution of deviations from mean star trail directions was studied on the basis of 105 star trails. It was found that about 93% of the trails yield a distribution in agreement with the normal law. About 4% of the star trails agree with the Charlier distribution.

Finite Element Simulation and Experimental Verification of Internal Stress of Quenched AISI 4140 Cylinders

NASA Astrophysics Data System (ADS)

Liu, Yu; Qin, Shengwei; Hao, Qingguo; Chen, Nailu; Zuo, Xunwei; Rong, Yonghua

2017-03-01

The study of internal stress in quenched AISI 4140 medium carbon steel is of importance in engineering. In this work, the finite element simulation (FES) was employed to predict the distribution of internal stress in quenched AISI 4140 cylinders with two sizes of diameter based on exponent-modified (Ex-Modified) normalized function. The results indicate that the FES based on Ex-Modified normalized function proposed is better consistent with X-ray diffraction measurements of the stress distribution than FES based on normalized function proposed by Abrassart, Desalos and Leblond, respectively, which is attributed that Ex-Modified normalized function better describes transformation plasticity. Effect of temperature distribution on the phase formation, the origin of residual stress distribution and effect of transformation plasticity function on the residual stress distribution were further discussed.

Smooth quantile normalization.

PubMed

Hicks, Stephanie C; Okrah, Kwame; Paulson, Joseph N; Quackenbush, John; Irizarry, Rafael A; Bravo, Héctor Corrada

2018-04-01

Between-sample normalization is a critical step in genomic data analysis to remove systematic bias and unwanted technical variation in high-throughput data. Global normalization methods are based on the assumption that observed variability in global properties is due to technical reasons and are unrelated to the biology of interest. For example, some methods correct for differences in sequencing read counts by scaling features to have similar median values across samples, but these fail to reduce other forms of unwanted technical variation. Methods such as quantile normalization transform the statistical distributions across samples to be the same and assume global differences in the distribution are induced by only technical variation. However, it remains unclear how to proceed with normalization if these assumptions are violated, for example, if there are global differences in the statistical distributions between biological conditions or groups, and external information, such as negative or control features, is not available. Here, we introduce a generalization of quantile normalization, referred to as smooth quantile normalization (qsmooth), which is based on the assumption that the statistical distribution of each sample should be the same (or have the same distributional shape) within biological groups or conditions, but allowing that they may differ between groups. We illustrate the advantages of our method on several high-throughput datasets with global differences in distributions corresponding to different biological conditions. We also perform a Monte Carlo simulation study to illustrate the bias-variance tradeoff and root mean squared error of qsmooth compared to other global normalization methods. A software implementation is available from https://github.com/stephaniehicks/qsmooth.

LOG-NORMAL DISTRIBUTION OF COSMIC VOIDS IN SIMULATIONS AND MOCKS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Russell, E.; Pycke, J.-R., E-mail: er111@nyu.edu, E-mail: jrp15@nyu.edu

2017-01-20

Following up on previous studies, we complete here a full analysis of the void size distributions of the Cosmic Void Catalog based on three different simulation and mock catalogs: dark matter (DM), haloes, and galaxies. Based on this analysis, we attempt to answer two questions: Is a three-parameter log-normal distribution a good candidate to satisfy the void size distributions obtained from different types of environments? Is there a direct relation between the shape parameters of the void size distribution and the environmental effects? In an attempt to answer these questions, we find here that all void size distributions of thesemore » data samples satisfy the three-parameter log-normal distribution whether the environment is dominated by DM, haloes, or galaxies. In addition, the shape parameters of the three-parameter log-normal void size distribution seem highly affected by environment, particularly existing substructures. Therefore, we show two quantitative relations given by linear equations between the skewness and the maximum tree depth, and between the variance of the void size distribution and the maximum tree depth, directly from the simulated data. In addition to this, we find that the percentage of voids with nonzero central density in the data sets has a critical importance. If the number of voids with nonzero central density reaches ≥3.84% in a simulation/mock sample, then a second population is observed in the void size distributions. This second population emerges as a second peak in the log-normal void size distribution at larger radius.« less

Time-independent models of asset returns revisited

NASA Astrophysics Data System (ADS)

Gillemot, L.; Töyli, J.; Kertesz, J.; Kaski, K.

2000-07-01

In this study we investigate various well-known time-independent models of asset returns being simple normal distribution, Student t-distribution, Lévy, truncated Lévy, general stable distribution, mixed diffusion jump, and compound normal distribution. For this we use Standard and Poor's 500 index data of the New York Stock Exchange, Helsinki Stock Exchange index data describing a small volatile market, and artificial data. The results indicate that all models, excluding the simple normal distribution, are, at least, quite reasonable descriptions of the data. Furthermore, the use of differences instead of logarithmic returns tends to make the data looking visually more Lévy-type distributed than it is. This phenomenon is especially evident in the artificial data that has been generated by an inflated random walk process.

Flexible mixture modeling via the multivariate t distribution with the Box-Cox transformation: an alternative to the skew-t distribution

PubMed Central

Lo, Kenneth

2011-01-01

Cluster analysis is the automated search for groups of homogeneous observations in a data set. A popular modeling approach for clustering is based on finite normal mixture models, which assume that each cluster is modeled as a multivariate normal distribution. However, the normality assumption that each component is symmetric is often unrealistic. Furthermore, normal mixture models are not robust against outliers; they often require extra components for modeling outliers and/or give a poor representation of the data. To address these issues, we propose a new class of distributions, multivariate t distributions with the Box-Cox transformation, for mixture modeling. This class of distributions generalizes the normal distribution with the more heavy-tailed t distribution, and introduces skewness via the Box-Cox transformation. As a result, this provides a unified framework to simultaneously handle outlier identification and data transformation, two interrelated issues. We describe an Expectation-Maximization algorithm for parameter estimation along with transformation selection. We demonstrate the proposed methodology with three real data sets and simulation studies. Compared with a wealth of approaches including the skew-t mixture model, the proposed t mixture model with the Box-Cox transformation performs favorably in terms of accuracy in the assignment of observations, robustness against model misspecification, and selection of the number of components. PMID:22125375

Flexible mixture modeling via the multivariate t distribution with the Box-Cox transformation: an alternative to the skew-t distribution.

PubMed

Lo, Kenneth; Gottardo, Raphael

2012-01-01

Cluster analysis is the automated search for groups of homogeneous observations in a data set. A popular modeling approach for clustering is based on finite normal mixture models, which assume that each cluster is modeled as a multivariate normal distribution. However, the normality assumption that each component is symmetric is often unrealistic. Furthermore, normal mixture models are not robust against outliers; they often require extra components for modeling outliers and/or give a poor representation of the data. To address these issues, we propose a new class of distributions, multivariate t distributions with the Box-Cox transformation, for mixture modeling. This class of distributions generalizes the normal distribution with the more heavy-tailed t distribution, and introduces skewness via the Box-Cox transformation. As a result, this provides a unified framework to simultaneously handle outlier identification and data transformation, two interrelated issues. We describe an Expectation-Maximization algorithm for parameter estimation along with transformation selection. We demonstrate the proposed methodology with three real data sets and simulation studies. Compared with a wealth of approaches including the skew-t mixture model, the proposed t mixture model with the Box-Cox transformation performs favorably in terms of accuracy in the assignment of observations, robustness against model misspecification, and selection of the number of components.

Constructing inverse probability weights for continuous exposures: a comparison of methods.

PubMed

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

A general approach to double-moment normalization of drop size distributions

NASA Astrophysics Data System (ADS)

Lee, G. W.; Sempere-Torres, D.; Uijlenhoet, R.; Zawadzki, I.

2003-04-01

Normalization of drop size distributions (DSDs) is re-examined here. First, we present an extension of scaling normalization using one moment of the DSD as a parameter (as introduced by Sempere-Torres et al, 1994) to a scaling normalization using two moments as parameters of the normalization. It is shown that the normalization of Testud et al. (2001) is a particular case of the two-moment scaling normalization. Thus, a unified vision of the question of DSDs normalization and a good model representation of DSDs is given. Data analysis shows that from the point of view of moment estimation least square regression is slightly more effective than moment estimation from the normalized average DSD.

A Bayesian Nonparametric Meta-Analysis Model

ERIC Educational Resources Information Center

Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G.

2015-01-01

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…

Type I error rates of rare single nucleotide variants are inflated in tests of association with non-normally distributed traits using simple linear regression methods.

PubMed

Schwantes-An, Tae-Hwi; Sung, Heejong; Sabourin, Jeremy A; Justice, Cristina M; Sorant, Alexa J M; Wilson, Alexander F

2016-01-01

In this study, the effects of (a) the minor allele frequency of the single nucleotide variant (SNV), (b) the degree of departure from normality of the trait, and (c) the position of the SNVs on type I error rates were investigated in the Genetic Analysis Workshop (GAW) 19 whole exome sequence data. To test the distribution of the type I error rate, 5 simulated traits were considered: standard normal and gamma distributed traits; 2 transformed versions of the gamma trait (log 10 and rank-based inverse normal transformations); and trait Q1 provided by GAW 19. Each trait was tested with 313,340 SNVs. Tests of association were performed with simple linear regression and average type I error rates were determined for minor allele frequency classes. Rare SNVs (minor allele frequency < 0.05) showed inflated type I error rates for non-normally distributed traits that increased as the minor allele frequency decreased. The inflation of average type I error rates increased as the significance threshold decreased. Normally distributed traits did not show inflated type I error rates with respect to the minor allele frequency for rare SNVs. There was no consistent effect of transformation on the uniformity of the distribution of the location of SNVs with a type I error.

Computation of distribution of minimum resolution for log-normal distribution of chromatographic peak heights.

PubMed

Davis, Joe M

2011-10-28

General equations are derived for the distribution of minimum resolution between two chromatographic peaks, when peak heights in a multi-component chromatogram follow a continuous statistical distribution. The derivation draws on published theory by relating the area under the distribution of minimum resolution to the area under the distribution of the ratio of peak heights, which in turn is derived from the peak-height distribution. Two procedures are proposed for the equations' numerical solution. The procedures are applied to the log-normal distribution, which recently was reported to describe the distribution of component concentrations in three complex natural mixtures. For published statistical parameters of these mixtures, the distribution of minimum resolution is similar to that for the commonly assumed exponential distribution of peak heights used in statistical-overlap theory. However, these two distributions of minimum resolution can differ markedly, depending on the scale parameter of the log-normal distribution. Theory for the computation of the distribution of minimum resolution is extended to other cases of interest. With the log-normal distribution of peak heights as an example, the distribution of minimum resolution is computed when small peaks are lost due to noise or detection limits, and when the height of at least one peak is less than an upper limit. The distribution of minimum resolution shifts slightly to lower resolution values in the first case and to markedly larger resolution values in the second one. The theory and numerical procedure are confirmed by Monte Carlo simulation. Copyright © 2011 Elsevier B.V. All rights reserved.

Interpreting the concordance statistic of a logistic regression model: relation to the variance and odds ratio of a continuous explanatory variable.

PubMed

Austin, Peter C; Steyerberg, Ewout W

2012-06-20

When outcomes are binary, the c-statistic (equivalent to the area under the Receiver Operating Characteristic curve) is a standard measure of the predictive accuracy of a logistic regression model. An analytical expression was derived under the assumption that a continuous explanatory variable follows a normal distribution in those with and without the condition. We then conducted an extensive set of Monte Carlo simulations to examine whether the expressions derived under the assumption of binormality allowed for accurate prediction of the empirical c-statistic when the explanatory variable followed a normal distribution in the combined sample of those with and without the condition. We also examine the accuracy of the predicted c-statistic when the explanatory variable followed a gamma, log-normal or uniform distribution in combined sample of those with and without the condition. Under the assumption of binormality with equality of variances, the c-statistic follows a standard normal cumulative distribution function with dependence on the product of the standard deviation of the normal components (reflecting more heterogeneity) and the log-odds ratio (reflecting larger effects). Under the assumption of binormality with unequal variances, the c-statistic follows a standard normal cumulative distribution function with dependence on the standardized difference of the explanatory variable in those with and without the condition. In our Monte Carlo simulations, we found that these expressions allowed for reasonably accurate prediction of the empirical c-statistic when the distribution of the explanatory variable was normal, gamma, log-normal, and uniform in the entire sample of those with and without the condition. The discriminative ability of a continuous explanatory variable cannot be judged by its odds ratio alone, but always needs to be considered in relation to the heterogeneity of the population.

Application of a truncated normal failure distribution in reliability testing

NASA Technical Reports Server (NTRS)

Groves, C., Jr.

1968-01-01

Statistical truncated normal distribution function is applied as a time-to-failure distribution function in equipment reliability estimations. Age-dependent characteristics of the truncated function provide a basis for formulating a system of high-reliability testing that effectively merges statistical, engineering, and cost considerations.

The transmembrane gradient of the dielectric constant influences the DPH lifetime distribution.

PubMed

Konopásek, I; Kvasnicka, P; Amler, E; Kotyk, A; Curatola, G

1995-11-06

The fluorescence lifetime distribution of 1,6-diphenyl-1,3,5-hexatriene (DPH) and 1-[4-(trimethylamino)phenyl]-6-phenyl-1,3,5-hexatriene (TMA-DPH) in egg-phosphatidylcholine liposomes was measured in normal and heavy water. The lower dielectric constant (by approximately 12%) of heavy water compared with normal water was employed to provide direct evidence that the drop of the dielectric constant along the membrane normal shifts the centers of the distribution of both DPH and TMA-DPH to higher values and sharpens the widths of the distribution. The profile of the dielectric constant along the membrane normal was not found to be a linear gradient (in contrast to [1]) but a more complex function. Presence of cholesterol in liposomes further shifted the center of the distributions to higher value and sharpened them. In addition, it resulted in a more gradient-like profile of the dielectric constant (i.e. linearization) along the normal of the membrane. The effect of the change of dielectric constant on the membrane proteins is discussed.

Noninvasive Characterization of Indeterminate Pulmonary Nodules Detected on Chest High-Resolution Computed Tomography

DTIC Science & Technology

2016-10-01

the nodule. The discriminability of benign and malignant nodules were analyzed using t- test and the normal distribution of the individual metric value...22 Surround Distribution Distribution of the 7 parenchymal exemplars (Normal, Honey comb, Reticular, Ground glass, mild low attenuation area...the distribution of honey comb, reticular and ground glass surrounding the nodule. 0.001

29 CFR 4044.73 - Lump sums and other alternative forms of distribution in lieu of annuities.

Code of Federal Regulations, 2010 CFR

2010-07-01

... distribution is the present value of the normal form of benefit provided by the plan payable at normal... 29 Labor 9 2010-07-01 2010-07-01 false Lump sums and other alternative forms of distribution in... Benefits and Assets Non-Trusteed Plans § 4044.73 Lump sums and other alternative forms of distribution in...

Detection and Parameter Estimation of Chirped Radar Signals.

DTIC Science & Technology

2000-01-10

Wigner - Ville distribution ( WVD ): The WVD belongs to the Cohen’s class of energy distributions ...length. 28 6. Pseudo Wigner - Ville distribution (PWVD): The PWVD introduces a time-window to the WVD definition, thereby reducing the interferences...Frequency normalized to sampling frequency 26 Figure V.2: Wigner - Ville distribution ; time normalized to the pulse length 28 Figure V.3:

Generalization of the normal-exponential model: exploration of a more accurate parametrisation for the signal distribution on Illumina BeadArrays.

PubMed

Plancade, Sandra; Rozenholc, Yves; Lund, Eiliv

2012-12-11

Illumina BeadArray technology includes non specific negative control features that allow a precise estimation of the background noise. As an alternative to the background subtraction proposed in BeadStudio which leads to an important loss of information by generating negative values, a background correction method modeling the observed intensities as the sum of the exponentially distributed signal and normally distributed noise has been developed. Nevertheless, Wang and Ye (2012) display a kernel-based estimator of the signal distribution on Illumina BeadArrays and suggest that a gamma distribution would represent a better modeling of the signal density. Hence, the normal-exponential modeling may not be appropriate for Illumina data and background corrections derived from this model may lead to wrong estimation. We propose a more flexible modeling based on a gamma distributed signal and a normal distributed background noise and develop the associated background correction, implemented in the R-package NormalGamma. Our model proves to be markedly more accurate to model Illumina BeadArrays: on the one hand, it is shown on two types of Illumina BeadChips that this model offers a more correct fit of the observed intensities. On the other hand, the comparison of the operating characteristics of several background correction procedures on spike-in and on normal-gamma simulated data shows high similarities, reinforcing the validation of the normal-gamma modeling. The performance of the background corrections based on the normal-gamma and normal-exponential models are compared on two dilution data sets, through testing procedures which represent various experimental designs. Surprisingly, we observe that the implementation of a more accurate parametrisation in the model-based background correction does not increase the sensitivity. These results may be explained by the operating characteristics of the estimators: the normal-gamma background correction offers an improvement in terms of bias, but at the cost of a loss in precision. This paper addresses the lack of fit of the usual normal-exponential model by proposing a more flexible parametrisation of the signal distribution as well as the associated background correction. This new model proves to be considerably more accurate for Illumina microarrays, but the improvement in terms of modeling does not lead to a higher sensitivity in differential analysis. Nevertheless, this realistic modeling makes way for future investigations, in particular to examine the characteristics of pre-processing strategies.

Logistic Approximation to the Normal: The KL Rationale

ERIC Educational Resources Information Center

Savalei, Victoria

2006-01-01

A rationale is proposed for approximating the normal distribution with a logistic distribution using a scaling constant based on minimizing the Kullback-Leibler (KL) information, that is, the expected amount of information available in a sample to distinguish between two competing distributions using a likelihood ratio (LR) test, assuming one of…

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.; Ashwworth, G. R.; Winter, W. R.

1980-01-01

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Descriptive Statistics for Modern Test Score Distributions: Skewness, Kurtosis, Discreteness, and Ceiling Effects

ERIC Educational Resources Information Center

Ho, Andrew D.; Yu, Carol C.

2015-01-01

Many statistical analyses benefit from the assumption that unconditional or conditional distributions are continuous and normal. More than 50 years ago in this journal, Lord and Cook chronicled departures from normality in educational tests, and Micerri similarly showed that the normality assumption is met rarely in educational and psychological…

Exact Interval Estimation, Power Calculation, and Sample Size Determination in Normal Correlation Analysis

ERIC Educational Resources Information Center

Shieh, Gwowen

2006-01-01

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…

Comparison of Multidimensional Item Response Models: Multivariate Normal Ability Distributions versus Multivariate Polytomous Ability Distributions. Research Report. ETS RR-08-45

ERIC Educational Resources Information Center

Haberman, Shelby J.; von Davier, Matthias; Lee, Yi-Hsuan

2008-01-01

Multidimensional item response models can be based on multivariate normal ability distributions or on multivariate polytomous ability distributions. For the case of simple structure in which each item corresponds to a unique dimension of the ability vector, some applications of the two-parameter logistic model to empirical data are employed to…

Statistical analysis of the 70 meter antenna surface distortions

NASA Technical Reports Server (NTRS)

Kiedron, K.; Chian, C. T.; Chuang, K. L.

1987-01-01

Statistical analysis of surface distortions of the 70 meter NASA/JPL antenna, located at Goldstone, was performed. The purpose of this analysis is to verify whether deviations due to gravity loading can be treated as quasi-random variables with normal distribution. Histograms of the RF pathlength error distribution for several antenna elevation positions were generated. The results indicate that the deviations from the ideal antenna surface are not normally distributed. The observed density distribution for all antenna elevation angles is taller and narrower than the normal density, which results in large positive values of kurtosis and a significant amount of skewness. The skewness of the distribution changes from positive to negative as the antenna elevation changes from zenith to horizon.

An inexact log-normal distribution-based stochastic chance-constrained model for agricultural water quality management

NASA Astrophysics Data System (ADS)

Wang, Yu; Fan, Jie; Xu, Ye; Sun, Wei; Chen, Dong

2018-05-01

In this study, an inexact log-normal-based stochastic chance-constrained programming model was developed for solving the non-point source pollution issues caused by agricultural activities. Compared to the general stochastic chance-constrained programming model, the main advantage of the proposed model is that it allows random variables to be expressed as a log-normal distribution, rather than a general normal distribution. Possible deviations in solutions caused by irrational parameter assumptions were avoided. The agricultural system management in the Erhai Lake watershed was used as a case study, where critical system factors, including rainfall and runoff amounts, show characteristics of a log-normal distribution. Several interval solutions were obtained under different constraint-satisfaction levels, which were useful in evaluating the trade-off between system economy and reliability. The applied results show that the proposed model could help decision makers to design optimal production patterns under complex uncertainties. The successful application of this model is expected to provide a good example for agricultural management in many other watersheds.

Scoring in genetically modified organism proficiency tests based on log-transformed results.

PubMed

Thompson, Michael; Ellison, Stephen L R; Owen, Linda; Mathieson, Kenneth; Powell, Joanne; Key, Pauline; Wood, Roger; Damant, Andrew P

2006-01-01

The study considers data from 2 UK-based proficiency schemes and includes data from a total of 29 rounds and 43 test materials over a period of 3 years. The results from the 2 schemes are similar and reinforce each other. The amplification process used in quantitative polymerase chain reaction determinations predicts a mixture of normal, binomial, and lognormal distributions dominated by the latter 2. As predicted, the study results consistently follow a positively skewed distribution. Log-transformation prior to calculating z-scores is effective in establishing near-symmetric distributions that are sufficiently close to normal to justify interpretation on the basis of the normal distribution.

Differential models of twin correlations in skew for body-mass index (BMI).

PubMed

Tsang, Siny; Duncan, Glen E; Dinescu, Diana; Turkheimer, Eric

2018-01-01

Body Mass Index (BMI), like most human phenotypes, is substantially heritable. However, BMI is not normally distributed; the skew appears to be structural, and increases as a function of age. Moreover, twin correlations for BMI commonly violate the assumptions of the most common variety of the classical twin model, with the MZ twin correlation greater than twice the DZ correlation. This study aimed to decompose twin correlations for BMI using more general skew-t distributions. Same sex MZ and DZ twin pairs (N = 7,086) from the community-based Washington State Twin Registry were included. We used latent profile analysis (LPA) to decompose twin correlations for BMI into multiple mixture distributions. LPA was performed using the default normal mixture distribution and the skew-t mixture distribution. Similar analyses were performed for height as a comparison. Our analyses are then replicated in an independent dataset. A two-class solution under the skew-t mixture distribution fits the BMI distribution for both genders. The first class consists of a relatively normally distributed, highly heritable BMI with a mean in the normal range. The second class is a positively skewed BMI in the overweight and obese range, with lower twin correlations. In contrast, height is normally distributed, highly heritable, and is well-fit by a single latent class. Results in the replication dataset were highly similar. Our findings suggest that two distinct processes underlie the skew of the BMI distribution. The contrast between height and weight is in accord with subjective psychological experience: both are under obvious genetic influence, but BMI is also subject to behavioral control, whereas height is not.

The Effect on Non-Normal Distributions on the Integrated Moving Average Model of Time-Series Analysis.

ERIC Educational Resources Information Center

Doerann-George, Judith

The Integrated Moving Average (IMA) model of time series, and the analysis of intervention effects based on it, assume random shocks which are normally distributed. To determine the robustness of the analysis to violations of this assumption, empirical sampling methods were employed. Samples were generated from three populations; normal,…

An Evaluation of Normal versus Lognormal Distribution in Data Description and Empirical Analysis

ERIC Educational Resources Information Center

Diwakar, Rekha

2017-01-01

Many existing methods of statistical inference and analysis rely heavily on the assumption that the data are normally distributed. However, the normality assumption is not fulfilled when dealing with data which does not contain negative values or are otherwise skewed--a common occurrence in diverse disciplines such as finance, economics, political…

Standard Error of Linear Observed-Score Equating for the NEAT Design with Nonnormally Distributed Data

ERIC Educational Resources Information Center

Zu, Jiyun; Yuan, Ke-Hai

2012-01-01

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

Computer program determines exact two-sided tolerance limits for normal distributions

NASA Technical Reports Server (NTRS)

Friedman, H. A.; Webb, S. R.

1968-01-01

Computer program determines by numerical integration the exact statistical two-sided tolerance limits, when the proportion between the limits is at least a specified number. The program is limited to situations in which the underlying probability distribution for the population sampled is the normal distribution with unknown mean and variance.

Normal versus Noncentral Chi-Square Asymptotics of Misspecified Models

ERIC Educational Resources Information Center

Chun, So Yeon; Shapiro, Alexander

2009-01-01

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods

ERIC Educational Resources Information Center

Zhong, Xiaoling; Yuan, Ke-Hai

2011-01-01

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

The Distribution of the Product Explains Normal Theory Mediation Confidence Interval Estimation.

PubMed

Kisbu-Sakarya, Yasemin; MacKinnon, David P; Miočević, Milica

2014-05-01

The distribution of the product has several useful applications. One of these applications is its use to form confidence intervals for the indirect effect as the product of 2 regression coefficients. The purpose of this article is to investigate how the moments of the distribution of the product explain normal theory mediation confidence interval coverage and imbalance. Values of the critical ratio for each random variable are used to demonstrate how the moments of the distribution of the product change across values of the critical ratio observed in research studies. Results of the simulation study showed that as skewness in absolute value increases, coverage decreases. And as skewness in absolute value and kurtosis increases, imbalance increases. The difference between testing the significance of the indirect effect using the normal theory versus the asymmetric distribution of the product is further illustrated with a real data example. This article is the first study to show the direct link between the distribution of the product and indirect effect confidence intervals and clarifies the results of previous simulation studies by showing why normal theory confidence intervals for indirect effects are often less accurate than those obtained from the asymmetric distribution of the product or from resampling methods.

Stick-slip behavior in a continuum-granular experiment.

PubMed

Geller, Drew A; Ecke, Robert E; Dahmen, Karin A; Backhaus, Scott

2015-12-01

We report moment distribution results from a laboratory experiment, similar in character to an isolated strike-slip earthquake fault, consisting of sheared elastic plates separated by a narrow gap filled with a two-dimensional granular medium. Local measurement of strain displacements of the plates at 203 spatial points located adjacent to the gap allows direct determination of the event moments and their spatial and temporal distributions. We show that events consist of spatially coherent, larger motions and spatially extended (noncoherent), smaller events. The noncoherent events have a probability distribution of event moment consistent with an M(-3/2) power law scaling with Poisson-distributed recurrence times. Coherent events have a log-normal moment distribution and mean temporal recurrence. As the applied normal pressure increases, there are more coherent events and their log-normal distribution broadens and shifts to larger average moment.

Improved Root Normal Size Distributions for Liquid Atomization

DTIC Science & Technology

2015-11-01

Jackson, Primary Breakup of Round Aerated- Liquid Jets in Supersonic Crossflows, Atomization and Sprays, 16(6), 657-672, 2006 H. C. Simmons, The...Breakup in Liquid - Gas Mixing Layers, Atomization and Sprays, 1, 421-440, 1991 P.-K. Wu, L.-K. Tseng, and G. M. Faeth, Primary Breakup in Gas / Liquid ...Improved Root Normal Size Distributions for Liquid Atomization Distribution Statement A. Approved for public release; distribution is unlimited

Bayesian alternative to the ISO-GUM's use of the Welch Satterthwaite formula

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

In certain disciplines, uncertainty is traditionally expressed as an interval about an estimate for the value of the measurand. Development of such uncertainty intervals with a stated coverage probability based on the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) requires a description of the probability distribution for the value of the measurand. The ISO-GUM propagates the estimates and their associated standard uncertainties for various input quantities through a linear approximation of the measurement equation to determine an estimate and its associated standard uncertainty for the value of the measurand. This procedure does not yield a probability distribution for the value of the measurand. The ISO-GUM suggests that under certain conditions motivated by the central limit theorem the distribution for the value of the measurand may be approximated by a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite (W-S) formula. The approximate t-distribution may then be used to develop an uncertainty interval with a stated coverage probability for the value of the measurand. We propose an approximate normal distribution based on a Bayesian uncertainty as an alternative to the t-distribution based on the W-S formula. A benefit of the approximate normal distribution based on a Bayesian uncertainty is that it greatly simplifies the expression of uncertainty by eliminating altogether the need for calculating effective degrees of freedom from the W-S formula. In the special case where the measurand is the difference between two means, each evaluated from statistical analyses of independent normally distributed measurements with unknown and possibly unequal variances, the probability distribution for the value of the measurand is known to be a Behrens-Fisher distribution. We compare the performance of the approximate normal distribution based on a Bayesian uncertainty and the approximate t-distribution based on the W-S formula with respect to the Behrens-Fisher distribution. The approximate normal distribution is simpler and better in this case. A thorough investigation of the relative performance of the two approximate distributions would require comparison for a range of measurement equations by numerical methods.

[Distribution of individuals by spontaneous frequencies of lymphocytes with micronuclei. Particularity and consequences].

PubMed

Serebrianyĭ, A M; Akleev, A V; Aleshchenko, A V; Antoshchina, M M; Kudriashova, O V; Riabchenko, N I; Semenova, L P; Pelevina, I I

2011-01-01

By micronucleus (MN) assay with cytokinetic cytochalasin B block, the mean frequency of blood lymphocytes with MN has been determined in 76 Moscow inhabitants, 35 people from Obninsk and 122 from Chelyabinsk region. In contrast to the distribution of individuals on spontaneous frequency of cells with aberrations, which was shown to be binomial (Kusnetzov et al., 1980), the distribution of individuals on the spontaneous frequency of cells with MN in all three massif can be acknowledged as log-normal (chi2 test). Distribution of individuals in the joined massifs (Moscow and Obninsk inhabitants) and in the unique massif of all inspected with great reliability must be acknowledged as log-normal (0.70 and 0.86 correspondingly), but it cannot be regarded as Poisson, binomial or normal. Taking into account that log-normal distribution of children by spontaneous frequency of lymphocytes with MN has been observed by the inspection of 473 children from different kindergartens in Moscow we can make the conclusion that log-normal is regularity inherent in this type of damage of lymphocytes genome. On the contrary the distribution of individuals on induced by irradiation in vitro lymphocytes with MN frequency in most cases must be acknowledged as normal. This distribution character points out that damage appearance in the individual (genomic instability) in a single lymphocytes increases the probability of the damage appearance in another lymphocytes. We can propose that damaged stem cells lymphocyte progenitor's exchange by information with undamaged cells--the type of the bystander effect process. It can also be supposed that transmission of damage to daughter cells occurs in the time of stem cells division.

Accuracy and uncertainty analysis of soil Bbf spatial distribution estimation at a coking plant-contaminated site based on normalization geostatistical technologies.

PubMed

Liu, Geng; Niu, Junjie; Zhang, Chao; Guo, Guanlin

2015-12-01

Data distribution is usually skewed severely by the presence of hot spots in contaminated sites. This causes difficulties for accurate geostatistical data transformation. Three types of typical normal distribution transformation methods termed the normal score, Johnson, and Box-Cox transformations were applied to compare the effects of spatial interpolation with normal distribution transformation data of benzo(b)fluoranthene in a large-scale coking plant-contaminated site in north China. Three normal transformation methods decreased the skewness and kurtosis of the benzo(b)fluoranthene, and all the transformed data passed the Kolmogorov-Smirnov test threshold. Cross validation showed that Johnson ordinary kriging has a minimum root-mean-square error of 1.17 and a mean error of 0.19, which was more accurate than the other two models. The area with fewer sampling points and that with high levels of contamination showed the largest prediction standard errors based on the Johnson ordinary kriging prediction map. We introduce an ideal normal transformation method prior to geostatistical estimation for severely skewed data, which enhances the reliability of risk estimation and improves the accuracy for determination of remediation boundaries.

Frequency distribution of lithium in leaves of Lycium andersonii

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romney, E.M.; Wallace, A.; Kinnear, J.

1977-01-01

Lycium andersonii A. Gray is an accumulator of Li. Assays were made of 200 samples of it collected from six different locations within the Northern Mojave Desert. Mean concentrations of Li varied from location to location and tended not to follow log/sub e/ normal distribution, and to follow a normal distribution only poorly. There was some negative skewness to the log/sub e/ distribution which did exist. The results imply that the variation in accumulation of Li depends upon native supply of Li. Possibly the Li supply and the ability of L. andersonii plants to accumulate it are both log/sub e/more » normally distributed. The mean leaf concentration of Li in all locations was 29 ..mu..g/g, but the maximum was 166 ..mu..g/g.« less

The stochastic distribution of available coefficient of friction for human locomotion of five different floor surfaces.

PubMed

Chang, Wen-Ruey; Matz, Simon; Chang, Chien-Chi

2014-05-01

The maximum coefficient of friction that can be supported at the shoe and floor interface without a slip is usually called the available coefficient of friction (ACOF) for human locomotion. The probability of a slip could be estimated using a statistical model by comparing the ACOF with the required coefficient of friction (RCOF), assuming that both coefficients have stochastic distributions. An investigation of the stochastic distributions of the ACOF of five different floor surfaces under dry, water and glycerol conditions is presented in this paper. One hundred friction measurements were performed on each floor surface under each surface condition. The Kolmogorov-Smirnov goodness-of-fit test was used to determine if the distribution of the ACOF was a good fit with the normal, log-normal and Weibull distributions. The results indicated that the ACOF distributions had a slightly better match with the normal and log-normal distributions than with the Weibull in only three out of 15 cases with a statistical significance. The results are far more complex than what had heretofore been published and different scenarios could emerge. Since the ACOF is compared with the RCOF for the estimate of slip probability, the distribution of the ACOF in seven cases could be considered a constant for this purpose when the ACOF is much lower or higher than the RCOF. A few cases could be represented by a normal distribution for practical reasons based on their skewness and kurtosis values without a statistical significance. No representation could be found in three cases out of 15. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Analysis of vector wind change with respect to time for Cape Kennedy, Florida

NASA Technical Reports Server (NTRS)

Adelfang, S. I.

1978-01-01

Multivariate analysis was used to determine the joint distribution of the four variables represented by the components of the wind vector at an initial time and after a specified elapsed time is hypothesized to be quadravariate normal; the fourteen statistics of this distribution, calculated from 15 years of twice-daily rawinsonde data are presented by monthly reference periods for each month from 0 to 27 km. The hypotheses that the wind component changes with respect to time is univariate normal, that the joint distribution of wind component change with respect to time is univariate normal, that the joint distribution of wind component changes is bivariate normal, and that the modulus of vector wind change is Rayleigh are tested by comparison with observed distributions. Statistics of the conditional bivariate normal distributions of vector wind at a future time given the vector wind at an initial time are derived. Wind changes over time periods from 1 to 5 hours, calculated from Jimsphere data, are presented. Extension of the theoretical prediction (based on rawinsonde data) of wind component change standard deviation to time periods of 1 to 5 hours falls (with a few exceptions) within the 95 percentile confidence band of the population estimate obtained from the Jimsphere sample data. The joint distributions of wind change components, conditional wind components, and 1 km vector wind shear change components are illustrated by probability ellipses at the 95 percentile level.

Interpreting the concordance statistic of a logistic regression model: relation to the variance and odds ratio of a continuous explanatory variable

PubMed Central

2012-01-01

Background When outcomes are binary, the c-statistic (equivalent to the area under the Receiver Operating Characteristic curve) is a standard measure of the predictive accuracy of a logistic regression model. Methods An analytical expression was derived under the assumption that a continuous explanatory variable follows a normal distribution in those with and without the condition. We then conducted an extensive set of Monte Carlo simulations to examine whether the expressions derived under the assumption of binormality allowed for accurate prediction of the empirical c-statistic when the explanatory variable followed a normal distribution in the combined sample of those with and without the condition. We also examine the accuracy of the predicted c-statistic when the explanatory variable followed a gamma, log-normal or uniform distribution in combined sample of those with and without the condition. Results Under the assumption of binormality with equality of variances, the c-statistic follows a standard normal cumulative distribution function with dependence on the product of the standard deviation of the normal components (reflecting more heterogeneity) and the log-odds ratio (reflecting larger effects). Under the assumption of binormality with unequal variances, the c-statistic follows a standard normal cumulative distribution function with dependence on the standardized difference of the explanatory variable in those with and without the condition. In our Monte Carlo simulations, we found that these expressions allowed for reasonably accurate prediction of the empirical c-statistic when the distribution of the explanatory variable was normal, gamma, log-normal, and uniform in the entire sample of those with and without the condition. Conclusions The discriminative ability of a continuous explanatory variable cannot be judged by its odds ratio alone, but always needs to be considered in relation to the heterogeneity of the population. PMID:22716998

Derivation of a Multiparameter Gamma Model for Analyzing the Residence-Time Distribution Function for Nonideal Flow Systems as an Alternative to the Advection-Dispersion Equation

DOE PAGES

Embry, Irucka; Roland, Victor; Agbaje, Oluropo; ...

2013-01-01

A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate themore » effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.« less

Testing models of parental investment strategy and offspring size in ants.

PubMed

Gilboa, Smadar; Nonacs, Peter

2006-01-01

Parental investment strategies can be fixed or flexible. A fixed strategy predicts making all offspring a single 'optimal' size. Dynamic models predict flexible strategies with more than one optimal size of offspring. Patterns in the distribution of offspring sizes may thus reveal the investment strategy. Static strategies should produce normal distributions. Dynamic strategies should often result in non-normal distributions. Furthermore, variance in morphological traits should be positively correlated with the length of developmental time the traits are exposed to environmental influences. Finally, the type of deviation from normality (i.e., skewed left or right, or platykurtic) should be correlated with the average offspring size. To test the latter prediction, we used simulations to detect significant departures from normality and categorize distribution types. Data from three species of ants strongly support the predicted patterns for dynamic parental investment. Offspring size distributions are often significantly non-normal. Traits fixed earlier in development, such as head width, are less variable than final body weight. The type of distribution observed correlates with mean female dry weight. The overall support for a dynamic parental investment model has implications for life history theory. Predicted conflicts over parental effort, sex investment ratios, and reproductive skew in cooperative breeders follow from assumptions of static parental investment strategies and omnipresent resource limitations. By contrast, with flexible investment strategies such conflicts can be either absent or maladaptive.

Comparative pharmacokinetic and tissue distribution profiles of four major bioactive components in normal and hepatic fibrosis rats after oral administration of Fuzheng Huayu recipe.

PubMed

Yang, Tao; Liu, Shan; Wang, Chang-Hong; Tao, Yan-Yan; Zhou, Hua; Liu, Cheng-Hai

2015-10-10

Fuzheng Huayu recipe (FZHY) is a herbal product for the treatment of liver fibrosis approved by the Chinese State Food and Drug Administration (SFDA), but its pharmacokinetics and tissue distribution had not been investigated. In this study, the liver fibrotic model was induced with intraperitoneal injection of dimethylnitrosamine (DMN), and FZHY was given orally to the model and normal rats. The plasma pharmacokinetics and tissue distribution profiles of four major bioactive components from FZHY were analyzed in the normal and fibrotic rat groups using an ultrahigh performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) method. Results revealed that the bioavailabilities of danshensu (DSS), salvianolic acid B (SAB) and rosmarinic acid (ROS) in liver fibrotic rats increased 1.49, 3.31 and 2.37-fold, respectively, compared to normal rats. There was no obvious difference in the pharmacokinetics of amygdalin (AMY) between the normal and fibrotic rats. The tissue distribution of DSS, SAB, and AMY trended to be mostly in the kidney and lung. The distribution of DSS, SAB, and AMY in liver tissue of the model rats was significantly decreased compared to the normal rats. Significant differences in the pharmacokinetics and tissue distribution profiles of DSS, ROS, SAB and AMY were observed in rats with hepatic fibrosis after oral administration of FZHY. These results provide a meaningful basis for developing a clinical dosage regimen in the treatment of hepatic fibrosis by FZHY. Copyright © 2015 Elsevier B.V. All rights reserved.

Discontinuity in the genetic and environmental causes of the intellectual disability spectrum.

PubMed

Reichenberg, Abraham; Cederlöf, Martin; McMillan, Andrew; Trzaskowski, Maciej; Kapra, Ori; Fruchter, Eyal; Ginat, Karen; Davidson, Michael; Weiser, Mark; Larsson, Henrik; Plomin, Robert; Lichtenstein, Paul

2016-01-26

Intellectual disability (ID) occurs in almost 3% of newborns. Despite substantial research, a fundamental question about its origin and links to intelligence (IQ) still remains. ID has been shown to be inherited and has been accepted as the extreme low of the normal IQ distribution. However, ID displays a complex pattern of inheritance. Previously, noninherited rare mutations were shown to contribute to severe ID risk in individual families, but in the majority of cases causes remain unknown. Common variants associated with ID risk in the population have not been systematically established. Here we evaluate the hypothesis, originally proposed almost 1 century ago, that most ID is caused by the same genetic and environmental influences responsible for the normal distribution of IQ, but that severe ID is not. We studied more than 1,000,000 sibling pairs and 9,000 twin pairs assessed for IQ and for the presence of ID. We evaluated whether genetic and environmental influences at the extremes of the distribution are different from those operating in the normal range. Here we show that factors influencing mild ID (lowest 3% of IQ distribution) were similar to those influencing IQ in the normal range. In contrast, the factors influencing severe ID (lowest 0.5% of IQ distribution) differ from those influencing mild ID or IQ scores in the normal range. Taken together, our results suggest that most severe ID is a distinct condition, qualitatively different from the preponderance of ID, which, in turn, represents the low extreme of the normal distribution of intelligence.

Discontinuity in the genetic and environmental causes of the intellectual disability spectrum

PubMed Central

Reichenberg, Abraham; Cederlöf, Martin; McMillan, Andrew; Trzaskowski, Maciej; Kapra, Ori; Fruchter, Eyal; Ginat, Karen; Davidson, Michael; Weiser, Mark; Larsson, Henrik; Plomin, Robert; Lichtenstein, Paul

2016-01-01

Intellectual disability (ID) occurs in almost 3% of newborns. Despite substantial research, a fundamental question about its origin and links to intelligence (IQ) still remains. ID has been shown to be inherited and has been accepted as the extreme low of the normal IQ distribution. However, ID displays a complex pattern of inheritance. Previously, noninherited rare mutations were shown to contribute to severe ID risk in individual families, but in the majority of cases causes remain unknown. Common variants associated with ID risk in the population have not been systematically established. Here we evaluate the hypothesis, originally proposed almost 1 century ago, that most ID is caused by the same genetic and environmental influences responsible for the normal distribution of IQ, but that severe ID is not. We studied more than 1,000,000 sibling pairs and 9,000 twin pairs assessed for IQ and for the presence of ID. We evaluated whether genetic and environmental influences at the extremes of the distribution are different from those operating in the normal range. Here we show that factors influencing mild ID (lowest 3% of IQ distribution) were similar to those influencing IQ in the normal range. In contrast, the factors influencing severe ID (lowest 0.5% of IQ distribution) differ from those influencing mild ID or IQ scores in the normal range. Taken together, our results suggest that most severe ID is a distinct condition, qualitatively different from the preponderance of ID, which, in turn, represents the low extreme of the normal distribution of intelligence. PMID:26711998

Comparison of CSF Distribution between Idiopathic Normal Pressure Hydrocephalus and Alzheimer Disease.

PubMed

Yamada, S; Ishikawa, M; Yamamoto, K

2016-07-01

CSF volumes in the basal cistern and Sylvian fissure are increased in both idiopathic normal pressure hydrocephalus and Alzheimer disease, though the differences in these volumes in idiopathic normal pressure hydrocephalus and Alzheimer disease have not been well-described. Using CSF segmentation and volume quantification, we compared the distribution of CSF in idiopathic normal pressure hydrocephalus and Alzheimer disease. CSF volumes were extracted from T2-weighted 3D spin-echo sequences on 3T MR imaging and quantified semi-automatically. We compared the volumes and ratios of the ventricles and subarachnoid spaces after classification in 30 patients diagnosed with idiopathic normal pressure hydrocephalus, 10 with concurrent idiopathic normal pressure hydrocephalus and Alzheimer disease, 18 with Alzheimer disease, and 26 control subjects 60 years of age or older. Brain to ventricle ratios at the anterior and posterior commissure levels and 3D volumetric convexity cistern to ventricle ratios were useful indices for the differential diagnosis of idiopathic normal pressure hydrocephalus or idiopathic normal pressure hydrocephalus with Alzheimer disease from Alzheimer disease, similar to the z-Evans index and callosal angle. The most distinctive characteristics of the CSF distribution in idiopathic normal pressure hydrocephalus were small convexity subarachnoid spaces and the large volume of the basal cistern and Sylvian fissure. The distribution of the subarachnoid spaces in the idiopathic normal pressure hydrocephalus with Alzheimer disease group was the most deformed among these 3 groups, though the mean ventricular volume of the idiopathic normal pressure hydrocephalus with Alzheimer disease group was intermediate between that of the idiopathic normal pressure hydrocephalus and Alzheimer disease groups. The z-axial expansion of the lateral ventricle and compression of the brain just above the ventricle were the common findings in the parameters for differentiating idiopathic normal pressure hydrocephalus from Alzheimer disease. © 2016 by American Journal of Neuroradiology.

Stochastic Frontier Model Approach for Measuring Stock Market Efficiency with Different Distributions

PubMed Central

Hasan, Md. Zobaer; Kamil, Anton Abdulbasah; Mustafa, Adli; Baten, Md. Azizul

2012-01-01

The stock market is considered essential for economic growth and expected to contribute to improved productivity. An efficient pricing mechanism of the stock market can be a driving force for channeling savings into profitable investments and thus facilitating optimal allocation of capital. This study investigated the technical efficiency of selected groups of companies of Bangladesh Stock Market that is the Dhaka Stock Exchange (DSE) market, using the stochastic frontier production function approach. For this, the authors considered the Cobb-Douglas Stochastic frontier in which the technical inefficiency effects are defined by a model with two distributional assumptions. Truncated normal and half-normal distributions were used in the model and both time-variant and time-invariant inefficiency effects were estimated. The results reveal that technical efficiency decreased gradually over the reference period and that truncated normal distribution is preferable to half-normal distribution for technical inefficiency effects. The value of technical efficiency was high for the investment group and low for the bank group, as compared with other groups in the DSE market for both distributions in time- varying environment whereas it was high for the investment group but low for the ceramic group as compared with other groups in the DSE market for both distributions in time-invariant situation. PMID:22629352

Stochastic frontier model approach for measuring stock market efficiency with different distributions.

PubMed

Hasan, Md Zobaer; Kamil, Anton Abdulbasah; Mustafa, Adli; Baten, Md Azizul

2012-01-01

The stock market is considered essential for economic growth and expected to contribute to improved productivity. An efficient pricing mechanism of the stock market can be a driving force for channeling savings into profitable investments and thus facilitating optimal allocation of capital. This study investigated the technical efficiency of selected groups of companies of Bangladesh Stock Market that is the Dhaka Stock Exchange (DSE) market, using the stochastic frontier production function approach. For this, the authors considered the Cobb-Douglas Stochastic frontier in which the technical inefficiency effects are defined by a model with two distributional assumptions. Truncated normal and half-normal distributions were used in the model and both time-variant and time-invariant inefficiency effects were estimated. The results reveal that technical efficiency decreased gradually over the reference period and that truncated normal distribution is preferable to half-normal distribution for technical inefficiency effects. The value of technical efficiency was high for the investment group and low for the bank group, as compared with other groups in the DSE market for both distributions in time-varying environment whereas it was high for the investment group but low for the ceramic group as compared with other groups in the DSE market for both distributions in time-invariant situation.

Exploring the Estimation of Examinee Locations Using Multidimensional Latent Trait Models under Different Distributional Assumptions

ERIC Educational Resources Information Center

Jang, Hyesuk

2014-01-01

This study aims to evaluate a multidimensional latent trait model to determine how well the model works in various empirical contexts. Contrary to the assumption of these latent trait models that the traits are normally distributed, situations in which the latent trait is not shaped with a normal distribution may occur (Sass et al, 2008; Woods…

SEM with Missing Data and Unknown Population Distributions Using Two-Stage ML: Theory and Its Application

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Lu, Laura

2008-01-01

This article provides the theory and application of the 2-stage maximum likelihood (ML) procedure for structural equation modeling (SEM) with missing data. The validity of this procedure does not require the assumption of a normally distributed population. When the population is normally distributed and all missing data are missing at random…

Asymptotic Distribution of the Likelihood Ratio Test Statistic for Sphericity of Complex Multivariate Normal Distribution.

DTIC Science & Technology

1981-08-01

RATIO TEST STATISTIC FOR SPHERICITY OF COMPLEX MULTIVARIATE NORMAL DISTRIBUTION* C. Fang P. R. Krishnaiah B. N. Nagarsenker** August 1981 Technical...and their applications in time sEries, the reader is referred to Krishnaiah (1976). Motivated by the applications in the area of inference on multiple...for practical purposes. Here, we note that Krishnaiah , Lee and Chang (1976) approxi- mated the null distribution of certain power of the likeli

Generating Multivariate Ordinal Data via Entropy Principles.

PubMed

Lee, Yen; Kaplan, David

2018-03-01

When conducting robustness research where the focus of attention is on the impact of non-normality, the marginal skewness and kurtosis are often used to set the degree of non-normality. Monte Carlo methods are commonly applied to conduct this type of research by simulating data from distributions with skewness and kurtosis constrained to pre-specified values. Although several procedures have been proposed to simulate data from distributions with these constraints, no corresponding procedures have been applied for discrete distributions. In this paper, we present two procedures based on the principles of maximum entropy and minimum cross-entropy to estimate the multivariate observed ordinal distributions with constraints on skewness and kurtosis. For these procedures, the correlation matrix of the observed variables is not specified but depends on the relationships between the latent response variables. With the estimated distributions, researchers can study robustness not only focusing on the levels of non-normality but also on the variations in the distribution shapes. A simulation study demonstrates that these procedures yield excellent agreement between specified parameters and those of estimated distributions. A robustness study concerning the effect of distribution shape in the context of confirmatory factor analysis shows that shape can affect the robust [Formula: see text] and robust fit indices, especially when the sample size is small, the data are severely non-normal, and the fitted model is complex.

Symmetric co-movement between Malaysia and Japan stock markets

NASA Astrophysics Data System (ADS)

Razak, Ruzanna Ab; Ismail, Noriszura

2017-04-01

The copula approach is a flexible tool known to capture linear, nonlinear, symmetric and asymmetric dependence between two or more random variables. It is often used as a co-movement measure between stock market returns. The information obtained from copulas such as the level of association of financial market during normal and bullish and bearish markets phases are useful for investment strategies and risk management. However, the study of co-movement between Malaysia and Japan markets are limited, especially using copulas. Hence, we aim to investigate the dependence structure between Malaysia and Japan capital markets for the period spanning from 2000 to 2012. In this study, we showed that the bivariate normal distribution is not suitable as the bivariate distribution or to present the dependence between Malaysia and Japan markets. Instead, Gaussian or normal copula was found a good fit to represent the dependence. From our findings, it can be concluded that simple distribution fitting such as bivariate normal distribution does not suit financial time series data, whose characteristics are often leptokurtic. The nature of the data is treated by ARMA-GARCH with heavy tail distributions and these can be associated with copula functions. Regarding the dependence structure between Malaysia and Japan markets, the findings suggest that both markets co-move concurrently during normal periods.

powerbox: Arbitrarily structured, arbitrary-dimension boxes and log-normal mocks

NASA Astrophysics Data System (ADS)

Murray, Steven G.

2018-05-01

powerbox creates density grids (or boxes) with an arbitrary two-point distribution (i.e. power spectrum). The software works in any number of dimensions, creates Gaussian or Log-Normal fields, and measures power spectra of output fields to ensure consistency. The primary motivation for creating the code was the simple creation of log-normal mock galaxy distributions, but the methodology can be used for other applications.

Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study.

PubMed

Chou, C P; Bentler, P M; Satorra, A

1991-11-01

Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.

Confidence bounds and hypothesis tests for normal distribution coefficients of variation

Treesearch

Steve Verrill; Richard A. Johnson

2007-01-01

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.

An Empirical Bayes Approach to Mantel-Haenszel DIF Analysis.

ERIC Educational Resources Information Center

Zwick, Rebecca; Thayer, Dorothy T.; Lewis, Charles

1999-01-01

Developed an empirical Bayes enhancement to Mantel-Haenszel (MH) analysis of differential item functioning (DIF) in which it is assumed that the MH statistics are normally distributed and that the prior distribution of underlying DIF parameters is also normal. (Author/SLD)

Distribution pattern of urine albumin creatinine ratio and the prevalence of high-normal levels in untreated asymptomatic non-diabetic hypertensive patients.

PubMed

Ohmaru, Natsuki; Nakatsu, Takaaki; Izumi, Reishi; Mashima, Keiichi; Toki, Misako; Kobayashi, Asako; Ogawa, Hiroko; Hirohata, Satoshi; Ikeda, Satoru; Kusachi, Shozo

2011-01-01

Even high-normal albuminuria is reportedly associated with cardiovascular events. We determined the urine albumin creatinine ratio (UACR) in spot urine samples and analyzed the UACR distribution and the prevalence of high-normal levels. The UACR was determined using immunoturbidimetry in 332 untreated asymptomatic non-diabetic Japanese patients with hypertension and in 69 control subjects. The microalbuminuria and macroalbuminuria levels were defined as a UCAR ≥30 and <300 µg/mg·creatinine and a UCAR ≥300 µg/mg·creatinine, respectively. The distribution patterns showed a highly skewed distribution for the lower levels, and a common logarithmic transformation produced a close fit to a Gaussian distribution with median, 25th and 75th percentile values of 22.6, 13.5 and 48.2 µg/mg·creatinine, respectively. When a high-normal UACR was set at >20 to <30 µg/mg·creatinine, 19.9% (66/332) of the hypertensive patients exhibited a high-normal UACR. Microalbuminuria and macroalbuminuria were observed in 36.1% (120/336) and 2.1% (7/332) of the patients, respectively. UACR was significantly correlated with the systolic and diastolic blood pressures and the pulse pressure. A stepwise multivariate analysis revealed that these pressures as well as age were independent factors that increased UACR. The UACR distribution exhibited a highly skewed pattern, with approximately 60% of untreated, non-diabetic hypertensive patients exhibiting a high-normal or larger UACR. Both hypertension and age are independent risk factors that increase the UACR. The present study indicated that a considerable percentage of patients require anti-hypertensive drugs with antiproteinuric effects at the start of treatment.

Sketching Curves for Normal Distributions--Geometric Connections

ERIC Educational Resources Information Center

Bosse, Michael J.

2006-01-01

Within statistics instruction, students are often requested to sketch the curve representing a normal distribution with a given mean and standard deviation. Unfortunately, these sketches are often notoriously imprecise. Poor sketches are usually the result of missing mathematical knowledge. This paper considers relationships which exist among…

Spatio-temporal precipitation climatology over complex terrain using a censored additive regression model.

PubMed

Stauffer, Reto; Mayr, Georg J; Messner, Jakob W; Umlauf, Nikolaus; Zeileis, Achim

2017-06-15

Flexible spatio-temporal models are widely used to create reliable and accurate estimates for precipitation climatologies. Most models are based on square root transformed monthly or annual means, where a normal distribution seems to be appropriate. This assumption becomes invalid on a daily time scale as the observations involve large fractions of zero observations and are limited to non-negative values. We develop a novel spatio-temporal model to estimate the full climatological distribution of precipitation on a daily time scale over complex terrain using a left-censored normal distribution. The results demonstrate that the new method is able to account for the non-normal distribution and the large fraction of zero observations. The new climatology provides the full climatological distribution on a very high spatial and temporal resolution, and is competitive with, or even outperforms existing methods, even for arbitrary locations.

On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process

NASA Astrophysics Data System (ADS)

Duarte Queirós, Sílvio M.

2012-07-01

We discuss the modification of the Kapteyn multiplicative process using the q-product of Borges [E.P. Borges, A possible deformed algebra and calculus inspired in nonextensive thermostatistics, Physica A 340 (2004) 95]. Depending on the value of the index q a generalisation of the log-Normal distribution is yielded. Namely, the distribution increases the tail for small (when q<1) or large (when q>1) values of the variable upon analysis. The usual log-Normal distribution is retrieved when q=1, which corresponds to the traditional Kapteyn multiplicative process. The main statistical features of this distribution as well as related random number generators and tables of quantiles of the Kolmogorov-Smirnov distance are presented. Finally, we illustrate the validity of this scenario by describing a set of variables of biological and financial origin.

Tools for Basic Statistical Analysis

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.

How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products

NASA Astrophysics Data System (ADS)

Annunziata, Mario Alberto; Petri, Alberto; Pontuale, Giorgio; Zaccaria, Andrea

2016-10-01

We have considered the statistical distributions of the volumes of 1131 products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries' economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramér-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy.

Economic values under inappropriate normal distribution assumptions.

PubMed

Sadeghi-Sefidmazgi, A; Nejati-Javaremi, A; Moradi-Shahrbabak, M; Miraei-Ashtiani, S R; Amer, P R

2012-08-01

The objectives of this study were to quantify the errors in economic values (EVs) for traits affected by cost or price thresholds when skewed or kurtotic distributions of varying degree are assumed to be normal and when data with a normal distribution is subject to censoring. EVs were estimated for a continuous trait with dichotomous economic implications because of a price premium or penalty arising from a threshold ranging between -4 and 4 standard deviations from the mean. In order to evaluate the impacts of skewness, positive and negative excess kurtosis, standard skew normal, Pearson and the raised cosine distributions were used, respectively. For the various evaluable levels of skewness and kurtosis, the results showed that EVs can be underestimated or overestimated by more than 100% when price determining thresholds fall within a range from the mean that might be expected in practice. Estimates of EVs were very sensitive to censoring or missing data. In contrast to practical genetic evaluation, economic evaluation is very sensitive to lack of normality and missing data. Although in some special situations, the presence of multiple thresholds may attenuate the combined effect of errors at each threshold point, in practical situations there is a tendency for a few key thresholds to dominate the EV, and there are many situations where errors could be compounded across multiple thresholds. In the development of breeding objectives for non-normal continuous traits influenced by value thresholds, it is necessary to select a transformation that will resolve problems of non-normality or consider alternative methods that are less sensitive to non-normality.

Normal bone and soft tissue distribution of fluorine-18-sodium fluoride and artifacts on 18F-NaF PET/CT bone scan: a pictorial review.

PubMed

Sarikaya, Ismet; Elgazzar, Abdelhamid H; Sarikaya, Ali; Alfeeli, Mahmoud

2017-10-01

Fluorine-18-sodium fluoride (F-NaF) PET/CT is a relatively new and high-resolution bone imaging modality. Since the use of F-NaF PET/CT has been increasing, it is important to accurately assess the images and be aware of normal distribution and major artifacts. In this pictorial review article, we will describe the normal uptake patterns of F-NaF in the bone tissues, particularly in complex structures, as well as its physiologic soft tissue distribution and certain artifacts seen on F-NaF PET/CT images.

Transferrin receptors in human tissues: their distribution and possible clinical relevance.

PubMed

Gatter, K C; Brown, G; Trowbridge, I S; Woolston, R E; Mason, D Y

1983-05-01

The distribution of transferrin receptors (TR) has been studied in a range of normal and malignant tissues using four monoclonal antibodies, BK19.9, B3/25, T56/14 and T58/1. In normal tissues TR was found in a limited number of sites, notably basal epidermis, the endocrine pancreas, hepatocytes, Kupffer cells, testis and pituitary. This restricted pattern of distribution may be relevant to the characteristic pattern of iron deposition in primary haemachromatosis. In contrast to this limited pattern of expression in normal tissue, the receptor was widely distributed in carcinomas, sarcomas and in samples from cases of Hodgkin's disease. This malignancy-associated expression of the receptor may play a role in the anaemia of advanced malignancy by competing with the bone marrow for serum iron.

Transferrin receptors in human tissues: their distribution and possible clinical relevance.

PubMed Central

Gatter, K C; Brown, G; Trowbridge, I S; Woolston, R E; Mason, D Y

1983-01-01

The distribution of transferrin receptors (TR) has been studied in a range of normal and malignant tissues using four monoclonal antibodies, BK19.9, B3/25, T56/14 and T58/1. In normal tissues TR was found in a limited number of sites, notably basal epidermis, the endocrine pancreas, hepatocytes, Kupffer cells, testis and pituitary. This restricted pattern of distribution may be relevant to the characteristic pattern of iron deposition in primary haemachromatosis. In contrast to this limited pattern of expression in normal tissue, the receptor was widely distributed in carcinomas, sarcomas and in samples from cases of Hodgkin's disease. This malignancy-associated expression of the receptor may play a role in the anaemia of advanced malignancy by competing with the bone marrow for serum iron. Images PMID:6302135

Statistical Power Analysis with Microsoft Excel: Normal Tests for One or Two Means as a Prelude to Using Non-Central Distributions to Calculate Power

ERIC Educational Resources Information Center

Texeira, Antonio; Rosa, Alvaro; Calapez, Teresa

2009-01-01

This article presents statistical power analysis (SPA) based on the normal distribution using Excel, adopting textbook and SPA approaches. The objective is to present the latter in a comparative way within a framework that is familiar to textbook level readers, as a first step to understand SPA with other distributions. The analysis focuses on the…

Spurious Latent Class Problem in the Mixed Rasch Model: A Comparison of Three Maximum Likelihood Estimation Methods under Different Ability Distributions

ERIC Educational Resources Information Center

Sen, Sedat

2018-01-01

Recent research has shown that over-extraction of latent classes can be observed in the Bayesian estimation of the mixed Rasch model when the distribution of ability is non-normal. This study examined the effect of non-normal ability distributions on the number of latent classes in the mixed Rasch model when estimated with maximum likelihood…

Differential distribution of blood and lymphatic vessels in the murine cornea.

PubMed

Ecoiffier, Tatiana; Yuen, Don; Chen, Lu

2010-05-01

Because of its unique characteristics, the cornea has been widely used for blood and lymphatic vessel research. However, whether limbal or corneal vessels are evenly distributed under normal or inflamed conditions has never been studied. The purpose of this study was to investigate this question and to examine whether and how the distribution patterns change during corneal inflammatory lymphangiogenesis (LG) and hemangiogenesis (HG). Corneal inflammatory LG and HG were induced in two most commonly used mouse strains, BALB/c and C57BL/6 (6-8 weeks of age), by a standardized two-suture placement model. Oriented flat-mount corneas together with the limbal tissues were used for immunofluorescence microscope studies. Blood and lymphatic vessels under normal and inflamed conditions were analyzed and quantified to compare their distributions. The data demonstrate, for the first time, greater distribution of both blood and lymphatic vessels in the nasal side in normal murine limbal areas. This nasal-dominant pattern was maintained during corneal inflammatory LG, whereas it was lost for HG. Blood and lymphatic vessels are not evenly distributed in normal limbal areas. Furthermore, corneal LG and HG respond differently to inflammatory stimuli. These new findings will shed some light on corneal physiology and pathogenesis and on the development of experimental models and therapeutic strategies for corneal diseases.

Three-dimensional finite analysis of acetabular contact pressure and contact area during normal walking.

PubMed

Wang, Guangye; Huang, Wenjun; Song, Qi; Liang, Jinfeng

2017-11-01

This study aims to analyze the contact areas and pressure distributions between the femoral head and mortar during normal walking using a three-dimensional finite element model (3D-FEM). Computed tomography (CT) scanning technology and a computer image processing system were used to establish the 3D-FEM. The acetabular mortar model was used to simulate the pressures during 32 consecutive normal walking phases and the contact areas at different phases were calculated. The distribution of the pressure peak values during the 32 consecutive normal walking phases was bimodal, which reached the peak (4.2 Mpa) at the initial phase where the contact area was significantly higher than that at the stepping phase. The sites that always kept contact were concentrated on the acetabular top and leaned inwards, while the anterior and posterior acetabular horns had no pressure concentration. The pressure distributions of acetabular cartilage at different phases were significantly different, the zone of increased pressure at the support phase distributed at the acetabular top area, while that at the stepping phase distributed in the inside of acetabular cartilage. The zones of increased contact pressure and the distributions of acetabular contact areas had important significance towards clinical researches, and could indicate the inductive factors of acetabular osteoarthritis. Copyright © 2016. Published by Elsevier Taiwan.

Predicting durations of online collective actions based on Peaks' heights

NASA Astrophysics Data System (ADS)

Lu, Peng; Nie, Shizhao; Wang, Zheng; Jing, Ziwei; Yang, Jianwu; Qi, Zhongxiang; Pujia, Wangmo

2018-02-01

Capturing the whole process of collective actions, the peak model contains four stages, including Prepare, Outbreak, Peak, and Vanish. Based on the peak model, one of the key variables, factors and parameters are further investigated in this paper, which is the rate between peaks and spans. Although the durations or spans and peaks' heights are highly diversified, it seems that the ratio between them is quite stable. If the rate's regularity is discovered, we can predict how long the collective action lasts and when it ends based on the peak's height. In this work, we combined mathematical simulations and empirical big data of 148 cases to explore the regularity of ratio's distribution. It is indicated by results of simulations that the rate has some regularities of distribution, which is not normal distribution. The big data has been collected from the 148 online collective actions and the whole processes of participation are recorded. The outcomes of empirical big data indicate that the rate seems to be closer to being log-normally distributed. This rule holds true for both the total cases and subgroups of 148 online collective actions. The Q-Q plot is applied to check the normal distribution of the rate's logarithm, and the rate's logarithm does follow the normal distribution.

Statistical analysis of content of Cs-137 in soils in Bansko-Razlog region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kobilarov, R. G., E-mail: rkobi@tu-sofia.bg

Statistical analysis of the data set consisting of the activity concentrations of {sup 137}Cs in soils in Bansko–Razlog region is carried out in order to establish the dependence of the deposition and the migration of {sup 137}Cs on the soil type. The descriptive statistics and the test of normality show that the data set have not normal distribution. Positively skewed distribution and possible outlying values of the activity of {sup 137}Cs in soils were observed. After reduction of the effects of outliers, the data set is divided into two parts, depending on the soil type. Test of normality of themore » two new data sets shows that they have a normal distribution. Ordinary kriging technique is used to characterize the spatial distribution of the activity of {sup 137}Cs over an area covering 40 km{sup 2} (whole Razlog valley). The result (a map of the spatial distribution of the activity concentration of {sup 137}Cs) can be used as a reference point for future studies on the assessment of radiological risk to the population and the erosion of soils in the study area.« less

Box-Cox transformation of firm size data in statistical analysis

NASA Astrophysics Data System (ADS)

Chen, Ting Ting; Takaishi, Tetsuya

2014-03-01

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions.

A comparison of minimum distance and maximum likelihood techniques for proportion estimation

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Schucany, W. R.; Lindsey, H.; Gray, H. L.

1982-01-01

The estimation of mixing proportions P sub 1, P sub 2,...P sub m in the mixture density f(x) = the sum of the series P sub i F sub i(X) with i = 1 to M is often encountered in agricultural remote sensing problems in which case the p sub i's usually represent crop proportions. In these remote sensing applications, component densities f sub i(x) have typically been assumed to be normally distributed, and parameter estimation has been accomplished using maximum likelihood (ML) techniques. Minimum distance (MD) estimation is examined as an alternative to ML where, in this investigation, both procedures are based upon normal components. Results indicate that ML techniques are superior to MD when component distributions actually are normal, while MD estimation provides better estimates than ML under symmetric departures from normality. When component distributions are not symmetric, however, it is seen that neither of these normal based techniques provides satisfactory results.

[Quantitative study of diesel/CNG buses exhaust particulate size distribution in a road tunnel].

PubMed

Zhu, Chun; Zhang, Xu

2010-10-01

Vehicle emission is one of main sources of fine/ultra-fine particles in many cities. This study firstly presents daily mean particle size distributions of mixed diesel/CNG buses traffic flow by 4 days consecutive real world measurement in an Australia road tunnel. Emission factors (EFs) of particle size distribution of diesel buses and CNG buses are obtained by MLR methods, particle distributions of diesel buses and CNG buses are observed as single accumulation mode and nuclei-mode separately. Particle size distributions of mixed traffic flow are decomposed by two log-normal fitting curves for each 30 min interval mean scans, the degrees of fitting between combined fitting curves and corresponding in-situ scans for totally 90 fitting scans are from 0.972 to 0.998. Finally particle size distributions of diesel buses and CNG buses are quantified by statistical whisker-box charts. For log-normal particle size distribution of diesel buses, accumulation mode diameters are 74.5-86.5 nm, geometric standard deviations are 1.88-2.05. As to log-normal particle size distribution of CNG buses, nuclei-mode diameters are 19.9-22.9 nm, geometric standard deviations are 1.27-1.3.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed.

The Theoretical Distribution of Evoked Brainstem Activity in Preterm, High-Risk, and Healthy Infants.

ERIC Educational Resources Information Center

Salamy, A.

1981-01-01

Determines the frequency distribution of Brainstem Auditory Evoked Potential variables (BAEP) for premature babies at different stages of development--normal newborns, infants, young children, and adults. The author concludes that the assumption of normality underlying most "standard" statistical analyses can be met for many BAEP…

Multivariate stochastic simulation with subjective multivariate normal distributions

Treesearch

P. J. Ince; J. Buongiorno

1991-01-01

In many applications of Monte Carlo simulation in forestry or forest products, it may be known that some variables are correlated. However, for simplicity, in most simulations it has been assumed that random variables are independently distributed. This report describes an alternative Monte Carlo simulation technique for subjectively assesed multivariate normal...

Discrete Latent Markov Models for Normally Distributed Response Data

ERIC Educational Resources Information Center

Schmittmann, Verena D.; Dolan, Conor V.; van der Maas, Han L. J.; Neale, Michael C.

2005-01-01

Van de Pol and Langeheine (1990) presented a general framework for Markov modeling of repeatedly measured discrete data. We discuss analogical single indicator models for normally distributed responses. In contrast to discrete models, which have been studied extensively, analogical continuous response models have hardly been considered. These…

Statistical analysis of multivariate atmospheric variables. [cloud cover

NASA Technical Reports Server (NTRS)

Tubbs, J. D.

1979-01-01

Topics covered include: (1) estimation in discrete multivariate distributions; (2) a procedure to predict cloud cover frequencies in the bivariate case; (3) a program to compute conditional bivariate normal parameters; (4) the transformation of nonnormal multivariate to near-normal; (5) test of fit for the extreme value distribution based upon the generalized minimum chi-square; (6) test of fit for continuous distributions based upon the generalized minimum chi-square; (7) effect of correlated observations on confidence sets based upon chi-square statistics; and (8) generation of random variates from specified distributions.

Investigation into the Use of Normal and Half-Normal Plots for Interpreting Results from Screening Experiments.

DTIC Science & Technology

1987-03-25

by Lloyd (1952) using generalized least squares instead of ordinary least squares, and by Wilk, % 20 Gnanadesikan , and Freeny (1963) using a maximum...plot. The half-normal distribution is a special case of the gamma distribution proposed by Wilk, Gnanadesikan , and Huyett (1962). VARIATIONS ON THE... Gnanadesikan , R. Probability plotting methods for the analysis of data. Biometrika, 1968, 55, 1-17. This paper describes and discusses graphical techniques

Antagonism Between Luminal and Caffeine, Studied by the Use of Radioisotopes; RECHERCHES SUR LES BARBITURIQUES RADIOACTIFS: LA DISTRIBUTION DU LUMINAL DANS L'ORGANISME ANIMAL EN PRESENCE DE CAFEINE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aliprandi, B.; Masironi, R.

1959-10-31

The normal pattern of distribution of luminal in the animal organism was determined in mice using a tracer technique. The effect of an antagonistic drug, e.g., caffeine, on this normal distribution pattern was studied. The results confirmed the hypothesis of the in vivo breaking of the barbituric ring. (J.S.R.)

A comparative study of the spatial distribution of mast cells and microvessels in the foetal, adult human thymus and thymoma.

PubMed

Raica, Marius; Cimpean, Anca Maria; Nico, Beatrice; Guidolin, Diego; Ribatti, Domenico

2010-02-01

Mast cells (MCs) are widely distributed in human and animal tissues and have been shown to play an important role in angiogenesis in normal and pathological conditions. Few data are available about the relationship between MCs and blood vessels in the normal human thymus, and there are virtually no data about their distribution and significance in thymoma. The aim of this study was to analyse the spatial distribution of MCs and microvessels in the normal foetal and adult thymus and thymoma. Twenty biopsy specimens of human thymus, including foetal and adult normal thymus and thymoma were analysed. Double staining with CD34 and mast cell tryptase was used to count both mast cells and microvessels in the same fields. Computer-assisted image analysis was performed to characterize the spatial distribution of MCs and blood vessels in selected specimens. Results demonstrated that MCs were localized exclusively to the medulla. Their number was significantly higher in thymoma specimens as compared with adult and foetal normal specimens respectively. In contrast the microvessel area was unchanged. The analysis of the spatial distribution and relationship between MCs and microvessels revealed that only in the thymoma specimens was there a significant spatial association between MCs and microvessels. Overall, these data suggest that MCs do not contribute significantly to the development of the vascular network in foetal and adult thymus, whereas in thymoma they show a close relationship to blood vessels. This could be an expression of their involvement not only in endothelial cells but also in tumour cell proliferation.

Measuring Treasury Bond Portfolio Risk and Portfolio Optimization with a Non-Gaussian Multivariate Model

NASA Astrophysics Data System (ADS)

Dong, Yijun

The research about measuring the risk of a bond portfolio and the portfolio optimization was relatively rare previously, because the risk factors of bond portfolios are not very volatile. However, this condition has changed recently. The 2008 financial crisis brought high volatility to the risk factors and the related bond securities, even if the highly rated U.S. treasury bonds. Moreover, the risk factors of bond portfolios show properties of fat-tailness and asymmetry like risk factors of equity portfolios. Therefore, we need to use advanced techniques to measure and manage risk of bond portfolios. In our paper, we first apply autoregressive moving average generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) model with multivariate normal tempered stable (MNTS) distribution innovations to predict risk factors of U.S. treasury bonds and statistically demonstrate that MNTS distribution has the ability to capture the properties of risk factors based on the goodness-of-fit tests. Then based on empirical evidence, we find that the VaR and AVaR estimated by assuming normal tempered stable distribution are more realistic and reliable than those estimated by assuming normal distribution, especially for the financial crisis period. Finally, we use the mean-risk portfolio optimization to minimize portfolios' potential risks. The empirical study indicates that the optimized bond portfolios have better risk-adjusted performances than the benchmark portfolios for some periods. Moreover, the optimized bond portfolios obtained by assuming normal tempered stable distribution have improved performances in comparison to the optimized bond portfolios obtained by assuming normal distribution.

Size distribution and sorption of polychlorinated biphenyls during haze episodes

NASA Astrophysics Data System (ADS)

Zhu, Qingqing; Liu, Guorui; Zheng, Minghui; Zhang, Xian; Gao, Lirong; Su, Guijin; Liang, Yong

2018-01-01

There is a lack of studies on the size distribution of polychlorinated biphenyls (PCBs) during haze days, and their sorption mechanisms on aerosol particles remain unclear. In this study, PCBs in particle-sized aerosols from urban atmospheres of Beijing, China were investigated during haze and normal days. The concentrations, gas/particle partitioning, size distribution, and associated human daily intake of PCBs via inhalation were compared during haze days and normal days. Compared with normal days, higher particle mass-associated PCB levels were measured during haze days. The concentrations of ∑PCBs in particulate fractions were 11.9-134 pg/m3 and 6.37-14.9 pg/m3 during haze days and normal days, respectively. PCBs increased with decreasing particle size (>10 μm, 10-2.5 μm, 2.5-1.0 μm, and ≤1.0 μm). During haze days, PCBs were overwhelmingly associated with a fine particle fraction of ≤1.0 μm (64.6%), while during normal days the contribution was 33.7%. Tetra-CBs were the largest contributors (51.8%-66.7%) both in the gas and particle fractions during normal days. The profiles in the gas fraction were conspicuously different than those in the PM fractions during haze days, with di-CBs predominating in the gas fraction and higher homologues (tetra-CBs, penta-CBs, and hexa-CBs) concurrently accounting for most of the PM fractions. The mean-normalized size distributions of particulate mass and PCBs exhibited unimodal patterns, and a similar trend was observed for PCBs during both days. They all tended to be in the PM fraction of 1.0-2.5 μm. Adsorption might be the predominating mechanism for the gas-particle partitioning of PCBs during haze days, whereas absorption might be dominative during normal days.

Validation of MCDS by comparison of predicted with experimental velocity distribution functions in rarefied normal shocks

NASA Technical Reports Server (NTRS)

Pham-Van-diep, Gerald C.; Erwin, Daniel A.

1989-01-01

Velocity distribution functions in normal shock waves in argon and helium are calculated using Monte Carlo direct simulation. These are compared with experimental results for argon at M = 7.18 and for helium at M = 1.59 and 20. For both argon and helium, the variable-hard-sphere (VHS) model is used for the elastic scattering cross section, with the velocity dependence derived from a viscosity-temperature power-law relationship in the way normally used by Bird (1976).

Asymptotic Normality Through Factorial Cumulants and Partition Identities

PubMed Central

Bobecka, Konstancja; Hitczenko, Paweł; López-Blázquez, Fernando; Rempała, Grzegorz; Wesołowski, Jacek

2013-01-01

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for ‘moments’ of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution. PMID:24591773

Confidence Intervals for True Scores Using the Skew-Normal Distribution

ERIC Educational Resources Information Center

Garcia-Perez, Miguel A.

2010-01-01

A recent comparative analysis of alternative interval estimation approaches and procedures has shown that confidence intervals (CIs) for true raw scores determined with the Score method--which uses the normal approximation to the binomial distribution--have actual coverage probabilities that are closest to their nominal level. It has also recently…

/sup 111/In desferal: a new radiopharmaceutical for abscess detection. [Distribution studies in normal and abscess-bearing laboratory animals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chandra, R.; Pierno, C.; Braunstein, P.

1978-09-01

Desferal was labeled with /sup 111/In and its distribution was studied in normal mice, rabbits bearing turpentine-induced abscesses, and rats bearing Staphyloccus aureus-induced abscesses. The results indicate that /sup 111/In Desferal may be used in abscess detection and localization.

Confidence bounds for normal and lognormal distribution coefficients of variation

Treesearch

Steve Verrill

2003-01-01

This paper compares the so-called exact approach for obtaining confidence intervals on normal distribution coefficients of variation to approximate methods. Approximate approaches were found to perform less well than the exact approach for large coefficients of variation and small sample sizes. Web-based computer programs are described for calculating confidence...

Sample size determination for logistic regression on a logit-normal distribution.

PubMed

Kim, Seongho; Heath, Elisabeth; Heilbrun, Lance

2017-06-01

Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.

Multifrequency Retrieval of Cloud Ice Particle Size Distributions

DTIC Science & Technology

2005-01-01

distribution ( Testud et al., 2001) to represent the PSD. The normalized gamma distribution has several advantages over a typical gamma PSD. A typical gamma...variation correlated with variation in ýL ( Testud et al., 2001). This variation on N, with P, requires a priori restrictions on the variance in R in...Geoscience & Rem. Sensing, 40, 541-549. Testud , J., S. Oury, R. A. Black, P. Amayenc, and X. Dou, 2001: The Concept of "Normalized" Distibution to Describe

Analyzing repeated measures semi-continuous data, with application to an alcohol dependence study.

PubMed

Liu, Lei; Strawderman, Robert L; Johnson, Bankole A; O'Quigley, John M

2016-02-01

Two-part random effects models (Olsen and Schafer,(1) Tooze et al.(2)) have been applied to repeated measures of semi-continuous data, characterized by a mixture of a substantial proportion of zero values and a skewed distribution of positive values. In the original formulation of this model, the natural logarithm of the positive values is assumed to follow a normal distribution with a constant variance parameter. In this article, we review and consider three extensions of this model, allowing the positive values to follow (a) a generalized gamma distribution, (b) a log-skew-normal distribution, and (c) a normal distribution after the Box-Cox transformation. We allow for the possibility of heteroscedasticity. Maximum likelihood estimation is shown to be conveniently implemented in SAS Proc NLMIXED. The performance of the methods is compared through applications to daily drinking records in a secondary data analysis from a randomized controlled trial of topiramate for alcohol dependence treatment. We find that all three models provide a significantly better fit than the log-normal model, and there exists strong evidence for heteroscedasticity. We also compare the three models by the likelihood ratio tests for non-nested hypotheses (Vuong(3)). The results suggest that the generalized gamma distribution provides the best fit, though no statistically significant differences are found in pairwise model comparisons. © The Author(s) 2012.

heterogeneous mixture distributions for multi-source extreme rainfall

NASA Astrophysics Data System (ADS)

Ouarda, T.; Shin, J.; Lee, T. S.

2013-12-01

Mixture distributions have been used to model hydro-meteorological variables showing mixture distributional characteristics, e.g. bimodality. Homogeneous mixture (HOM) distributions (e.g. Normal-Normal and Gumbel-Gumbel) have been traditionally applied to hydro-meteorological variables. However, there is no reason to restrict the mixture distribution as the combination of one identical type. It might be beneficial to characterize the statistical behavior of hydro-meteorological variables from the application of heterogeneous mixture (HTM) distributions such as Normal-Gamma. In the present work, we focus on assessing the suitability of HTM distributions for the frequency analysis of hydro-meteorological variables. In the present work, in order to estimate the parameters of HTM distributions, the meta-heuristic algorithm (Genetic Algorithm) is employed to maximize the likelihood function. In the present study, a number of distributions are compared, including the Gamma-Extreme value type-one (EV1) HTM distribution, the EV1-EV1 HOM distribution, and EV1 distribution. The proposed distribution models are applied to the annual maximum precipitation data in South Korea. The Akaike Information Criterion (AIC), the root mean squared errors (RMSE) and the log-likelihood are used as measures of goodness-of-fit of the tested distributions. Results indicate that the HTM distribution (Gamma-EV1) presents the best fitness. The HTM distribution shows significant improvement in the estimation of quantiles corresponding to the 20-year return period. It is shown that extreme rainfall in the coastal region of South Korea presents strong heterogeneous mixture distributional characteristics. Results indicate that HTM distributions are a good alternative for the frequency analysis of hydro-meteorological variables when disparate statistical characteristics are presented.

Bidisperse and polydisperse suspension rheology at large solid fraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pednekar, Sidhant; Chun, Jaehun; Morris, Jeffrey F.

At the same solid volume fraction, bidisperse and polydisperse suspensions display lower viscosities, and weaker normal stress response, compared to monodisperse suspensions. The reduction of viscosity associated with size distribution can be explained by an increase of the maximum flowable, or jamming, solid fraction. In this work, concentrated or "dense" suspensions are simulated under strong shearing, where thermal motion and repulsive forces are negligible, but we allow for particle contact with a mild frictional interaction with interparticle friction coefficient of 0.2. Aspects of bidisperse suspension rheology are first revisited to establish that the approach reproduces established trends; the study ofmore » bidisperse suspensions at size ratios of large to small particle radii (2 to 4) shows that a minimum in the viscosity occurs for zeta slightly above 0.5, where zeta=phi_{large}/phi is the fraction of the total solid volume occupied by the large particles. The simple shear flows of polydisperse suspensions with truncated normal and log normal size distributions, and bidisperse suspensions which are statistically equivalent with these polydisperse cases up to third moment of the size distribution, are simulated and the rheologies are extracted. Prior work shows that such distributions with equivalent low-order moments have similar phi_{m}, and the rheological behaviors of normal, log normal and bidisperse cases are shown to be in close agreement for a wide range of standard deviation in particle size, with standard correlations which are functionally dependent on phi/phi_{m} providing excellent agreement with the rheology found in simulation. The close agreement of both viscosity and normal stress response between bi- and polydisperse suspensions demonstrates the controlling in influence of the maximum packing fraction in noncolloidal suspensions. Microstructural investigations and the stress distribution according to particle size are also presented.« less

Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

NASA Astrophysics Data System (ADS)

Jiang, Quan; Zhong, Shan; Cui, Jie; Feng, Xia-Ting; Song, Leibo

2016-12-01

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress-strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble's probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young's elastic modulus and Poisson's ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.

Probability density function of non-reactive solute concentration in heterogeneous porous formations.

PubMed

Bellin, Alberto; Tonina, Daniele

2007-10-30

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.

An evaluation of procedures to estimate monthly precipitation probabilities

NASA Astrophysics Data System (ADS)

Legates, David R.

1991-01-01

Many frequency distributions have been used to evaluate monthly precipitation probabilities. Eight of these distributions (including Pearson type III, extreme value, and transform normal probability density functions) are comparatively examined to determine their ability to represent accurately variations in monthly precipitation totals for global hydroclimatological analyses. Results indicate that a modified version of the Box-Cox transform-normal distribution more adequately describes the 'true' precipitation distribution than does any of the other methods. This assessment was made using a cross-validation procedure for a global network of 253 stations for which at least 100 years of monthly precipitation totals were available.

A spatial scan statistic for survival data based on Weibull distribution.

PubMed

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

The spatial scan statistic has been developed as a geographical cluster detection analysis tool for different types of data sets such as Bernoulli, Poisson, ordinal, normal and exponential. We propose a scan statistic for survival data based on Weibull distribution. It may also be used for other survival distributions, such as exponential, gamma, and log normal. The proposed method is applied on the survival data of tuberculosis patients for the years 2004-2005 in Nainital district of Uttarakhand, India. Simulation studies reveal that the proposed method performs well for different survival distribution functions. Copyright © 2013 John Wiley & Sons, Ltd.

A novel gamma-fitting statistical method for anti-drug antibody assays to establish assay cut points for data with non-normal distribution.

PubMed

Schlain, Brian; Amaravadi, Lakshmi; Donley, Jean; Wickramasekera, Ananda; Bennett, Donald; Subramanyam, Meena

2010-01-31

In recent years there has been growing recognition of the impact of anti-drug or anti-therapeutic antibodies (ADAs, ATAs) on the pharmacokinetic and pharmacodynamic behavior of the drug, which ultimately affects drug exposure and activity. These anti-drug antibodies can also impact safety of the therapeutic by inducing a range of reactions from hypersensitivity to neutralization of the activity of an endogenous protein. Assessments of immunogenicity, therefore, are critically dependent on the bioanalytical method used to test samples, in which a positive versus negative reactivity is determined by a statistically derived cut point based on the distribution of drug naïve samples. For non-normally distributed data, a novel gamma-fitting method for obtaining assay cut points is presented. Non-normal immunogenicity data distributions, which tend to be unimodal and positively skewed, can often be modeled by 3-parameter gamma fits. Under a gamma regime, gamma based cut points were found to be more accurate (closer to their targeted false positive rates) compared to normal or log-normal methods and more precise (smaller standard errors of cut point estimators) compared with the nonparametric percentile method. Under a gamma regime, normal theory based methods for estimating cut points targeting a 5% false positive rate were found in computer simulation experiments to have, on average, false positive rates ranging from 6.2 to 8.3% (or positive biases between +1.2 and +3.3%) with bias decreasing with the magnitude of the gamma shape parameter. The log-normal fits tended, on average, to underestimate false positive rates with negative biases as large a -2.3% with absolute bias decreasing with the shape parameter. These results were consistent with the well known fact that gamma distributions become less skewed and closer to a normal distribution as their shape parameters increase. Inflated false positive rates, especially in a screening assay, shifts the emphasis to confirm test results in a subsequent test (confirmatory assay). On the other hand, deflated false positive rates in the case of screening immunogenicity assays will not meet the minimum 5% false positive target as proposed in the immunogenicity assay guidance white papers. Copyright 2009 Elsevier B.V. All rights reserved.

Size distribution of submarine landslides along the U.S. Atlantic margin

USGS Publications Warehouse

Chaytor, J.D.; ten Brink, Uri S.; Solow, A.R.; Andrews, B.D.

2009-01-01

Assessment of the probability for destructive landslide-generated tsunamis depends on the knowledge of the number, size, and frequency of large submarine landslides. This paper investigates the size distribution of submarine landslides along the U.S. Atlantic continental slope and rise using the size of the landslide source regions (landslide failure scars). Landslide scars along the margin identified in a detailed bathymetric Digital Elevation Model (DEM) have areas that range between 0.89??km2 and 2410??km2 and volumes between 0.002??km3 and 179??km3. The area to volume relationship of these failure scars is almost linear (inverse power-law exponent close to 1), suggesting a fairly uniform failure thickness of a few 10s of meters in each event, with only rare, deep excavating landslides. The cumulative volume distribution of the failure scars is very well described by a log-normal distribution rather than by an inverse power-law, the most commonly used distribution for both subaerial and submarine landslides. A log-normal distribution centered on a volume of 0.86??km3 may indicate that landslides preferentially mobilize a moderate amount of material (on the order of 1??km3), rather than large landslides or very small ones. Alternatively, the log-normal distribution may reflect an inverse power law distribution modified by a size-dependent probability of observing landslide scars in the bathymetry data. If the latter is the case, an inverse power-law distribution with an exponent of 1.3 ?? 0.3, modified by a size-dependent conditional probability of identifying more failure scars with increasing landslide size, fits the observed size distribution. This exponent value is similar to the predicted exponent of 1.2 ?? 0.3 for subaerial landslides in unconsolidated material. Both the log-normal and modified inverse power-law distributions of the observed failure scar volumes suggest that large landslides, which have the greatest potential to generate damaging tsunamis, occur infrequently along the margin. ?? 2008 Elsevier B.V.

Velocity-Map Imaging for Emittance Characterization of Multiphoton Electron Emission from a Gold Surface

NASA Astrophysics Data System (ADS)

Ye, Hong; Trippel, Sebastian; Di Fraia, Michele; Fallahi, Arya; Mücke, Oliver D.; Kärtner, Franz X.; Küpper, Jochen

2018-04-01

A velocity-map-imaging spectrometer is demonstrated to characterize the normalized emittance (root-mean-square, rms) of photoemitted electron bunches. Both the two-dimensional spatial distribution and the projected velocity distribution images of photoemitted electrons are recorded by the detection system and analyzed to obtain the normalized emittance (rms). With the presented distribution function of the electron photoemission angles, a mathematical method is implemented to reconstruct the three-dimensional velocity distribution. As a first example, multiphoton emission from a planar Au surface is studied via irradiation at a glancing angle by intense 45-fs laser pulses at a central wavelength of 800 nm. The reconstructed energy distribution agrees very well with the Berglund-Spicer theory of photoemission. The normalized emittance (rms) of the intrinsic electron bunch is characterized to be 128 and 14 nm rad in the X and Y directions, respectively. The demonstrated imaging spectrometer has the ability to characterize the normalized emittance (rms) in a few minutes with a fine energy resolution of 0.2 meV in the image center and will, thereby, foster the further development of x-ray free-electron-laser injectors and ultrafast electron diffraction, and it opens up opportunities for studying correlated electron emission from surfaces and vacuum nanoelectronic devices.

Checking distributional assumptions for pharmacokinetic summary statistics based on simulations with compartmental models.

PubMed

Shen, Meiyu; Russek-Cohen, Estelle; Slud, Eric V

2016-08-12

Bioequivalence (BE) studies are an essential part of the evaluation of generic drugs. The most common in vivo BE study design is the two-period two-treatment crossover design. AUC (area under the concentration-time curve) and Cmax (maximum concentration) are obtained from the observed concentration-time profiles for each subject from each treatment under each sequence. In the BE evaluation of pharmacokinetic crossover studies, the normality of the univariate response variable, e.g. log(AUC) 1 or log(Cmax), is often assumed in the literature without much evidence. Therefore, we investigate the distributional assumption of the normality of response variables, log(AUC) and log(Cmax), by simulating concentration-time profiles from two-stage pharmacokinetic models (commonly used in pharmacokinetic research) for a wide range of pharmacokinetic parameters and measurement error structures. Our simulations show that, under reasonable distributional assumptions on the pharmacokinetic parameters, log(AUC) has heavy tails and log(Cmax) is skewed. Sensitivity analyses are conducted to investigate how the distribution of the standardized log(AUC) (or the standardized log(Cmax)) for a large number of simulated subjects deviates from normality if distributions of errors in the pharmacokinetic model for plasma concentrations deviate from normality and if the plasma concentration can be described by different compartmental models.

Extreme Mean and Its Applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.

1979-01-01

Extreme value statistics obtained from normally distributed data are considered. An extreme mean is defined as the mean of p-th probability truncated normal distribution. An unbiased estimate of this extreme mean and its large sample distribution are derived. The distribution of this estimate even for very large samples is found to be nonnormal. Further, as the sample size increases, the variance of the unbiased estimate converges to the Cramer-Rao lower bound. The computer program used to obtain the density and distribution functions of the standardized unbiased estimate, and the confidence intervals of the extreme mean for any data are included for ready application. An example is included to demonstrate the usefulness of extreme mean application.

Controls of earthquake faulting style on near field landslide triggering: The role of coseismic slip

NASA Astrophysics Data System (ADS)

Tatard, L.; Grasso, J. R.

2013-06-01

compare the spatial distributions of seven databases of landslides triggered by Mw=5.6-7.9 earthquakes, using distances normalized by the earthquake fault length. We show that the normalized landslide distance distributions collapse, i.e., the normalized distance distributions overlap whatever the size of the earthquake, separately for the events associated with dip-slip, buried-faulting earthquakes, and surface-faulting earthquakes. The dip-slip earthquakes triggered landslides at larger normalized distances than the oblique-slip event of Loma Prieta. We further identify that the surface-faulting earthquakes of Wenchuan, Chi-Chi, and Kashmir triggered landslides at normalized distances smaller than the ones expected from their Mw ≥ 7.6 magnitudes. These results support a control of the seismic slip (through amplitude, rake, and surface versus buried slip) on the distances at which landslides are triggered. In terms of coseismic landslide management in mountainous areas, our results allow us to propose distances at which 95 and 75% of landslides will be triggered as a function of the earthquake focal mechanism.

Using an APOS Framework to Understand Teachers' Responses to Questions on the Normal Distribution

ERIC Educational Resources Information Center

Bansilal, Sarah

2014-01-01

This study is an exploration of teachers' engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an "unknown percentage" problem, which required the application…

CAN'T MISS--conquer any number task by making important statistics simple. Part 2. Probability, populations, samples, and normal distributions.

PubMed

Hansen, John P

2003-01-01

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.

A Posteriori Correction of Forecast and Observation Error Variances

NASA Technical Reports Server (NTRS)

Rukhovets, Leonid

2005-01-01

Proposed method of total observation and forecast error variance correction is based on the assumption about normal distribution of "observed-minus-forecast" residuals (O-F), where O is an observed value and F is usually a short-term model forecast. This assumption can be accepted for several types of observations (except humidity) which are not grossly in error. Degree of nearness to normal distribution can be estimated by the symmetry or skewness (luck of symmetry) a(sub 3) = mu(sub 3)/sigma(sup 3) and kurtosis a(sub 4) = mu(sub 4)/sigma(sup 4) - 3 Here mu(sub i) = i-order moment, sigma is a standard deviation. It is well known that for normal distribution a(sub 3) = a(sub 4) = 0.

Distribution Characteristics of Air-Bone Gaps – Evidence of Bias in Manual Audiometry

PubMed Central

Margolis, Robert H.; Wilson, Richard H.; Popelka, Gerald R.; Eikelboom, Robert H.; Swanepoel, De Wet; Saly, George L.

2015-01-01

Objective Five databases were mined to examine distributions of air-bone gaps obtained by automated and manual audiometry. Differences in distribution characteristics were examined for evidence of influences unrelated to the audibility of test signals. Design The databases provided air- and bone-conduction thresholds that permitted examination of air-bone gap distributions that were free of ceiling and floor effects. Cases with conductive hearing loss were eliminated based on air-bone gaps, tympanometry, and otoscopy, when available. The analysis is based on 2,378,921 threshold determinations from 721,831 subjects from five databases. Results Automated audiometry produced air-bone gaps that were normally distributed suggesting that air- and bone-conduction thresholds are normally distributed. Manual audiometry produced air-bone gaps that were not normally distributed and show evidence of biasing effects of assumptions of expected results. In one database, the form of the distributions showed evidence of inclusion of conductive hearing losses. Conclusions Thresholds obtained by manual audiometry show tester bias effects from assumptions of the patient’s hearing loss characteristics. Tester bias artificially reduces the variance of bone-conduction thresholds and the resulting air-bone gaps. Because the automated method is free of bias from assumptions of expected results, these distributions are hypothesized to reflect the true variability of air- and bone-conduction thresholds and the resulting air-bone gaps. PMID:26627469

Bayes classification of terrain cover using normalized polarimetric data

NASA Technical Reports Server (NTRS)

Yueh, H. A.; Swartz, A. A.; Kong, J. A.; Shin, R. T.; Novak, L. M.

1988-01-01

The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function. The general form of the distance measure for the NPC is also obtained. It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained. A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions. The probability of error for the NPC is compared with those of several other single-feature classifiers. The classification error of NPCs is shown to be independent of the normalization function.

Distribution of CD163-positive cell and MHC class II-positive cell in the normal equine uveal tract.

PubMed

Sano, Yuto; Matsuda, Kazuya; Okamoto, Minoru; Takehana, Kazushige; Hirayama, Kazuko; Taniyama, Hiroyuki

2016-02-01

Antigen-presenting cells (APCs) in the uveal tract participate in ocular immunity including immune homeostasis and the pathogenesis of uveitis. In horses, although uveitis is the most common ocular disorder, little is known about ocular immunity, such as the distribution of APCs. In this study, we investigated the distribution of CD163-positive and MHC II-positive cells in the normal equine uveal tract using an immunofluorescence technique. Eleven eyes from 10 Thoroughbred horses aged 1 to 24 years old were used. Indirect immunofluorescence was performed using the primary antibodies CD163, MHC class II (MHC II) and CD20. To demonstrate the site of their greatest distribution, positive cells were manually counted in 3 different parts of the uveal tract (ciliary body, iris and choroid), and their average number was assessed by statistical analysis. The distribution of pleomorphic CD163- and MHC II-expressed cells was detected throughout the equine uveal tract, but no CD20-expressed cells were detected. The statistical analysis demonstrated the distribution of CD163- and MHC II-positive cells focusing on the ciliary body. These results demonstrated that the ciliary body is the largest site of their distribution in the normal equine uveal tract, and the ciliary body is considered to play important roles in uveal and/or ocular immune homeostasis. The data provided in this study will help further understanding of equine ocular immunity in the normal state and might be beneficial for understanding of mechanisms of ocular disorders, such as equine uveitis.

Confounding environmental colour and distribution shape leads to underestimation of population extinction risk.

PubMed

Fowler, Mike S; Ruokolainen, Lasse

2013-01-01

The colour of environmental variability influences the size of population fluctuations when filtered through density dependent dynamics, driving extinction risk through dynamical resonance. Slow fluctuations (low frequencies) dominate in red environments, rapid fluctuations (high frequencies) in blue environments and white environments are purely random (no frequencies dominate). Two methods are commonly employed to generate the coloured spatial and/or temporal stochastic (environmental) series used in combination with population (dynamical feedback) models: autoregressive [AR(1)] and sinusoidal (1/f) models. We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models. Increasing variability of sample Skewness and Kurtosis and decreasing mean Kurtosis of these series alter the frequency distribution shape of the realised values of the coloured stochastic processes. These changes in distribution shape alter patterns in the probability of single and series of extreme conditions. We show that the reduced extinction risk for undercompensating (slow growing) populations in red environments previously predicted with traditional 1/f methods is an artefact of changes in the distribution shapes of the environmental series. This is demonstrated by comparison with coloured series controlled to be normally distributed using spectral mimicry. Changes in the distribution shape that arise using traditional methods lead to underestimation of extinction risk in normally distributed, red 1/f environments. AR(1) methods also underestimate extinction risks in traditionally generated red environments. This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations. We must let the characteristics of known natural environmental covariates (e.g., colour and distribution shape) guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.

Polymorphic mountain whitefish (Prosopium williamsoni) in a coastal riverscape: size class assemblages, distribution, and habitat associations

USGS Publications Warehouse

Starr, James C.; Torgersen, Christian E.

2015-01-01

We compared the assemblage structure, spatial distributions, and habitat associations of mountain whitefish (Prosopium williamsoni) morphotypes and size classes. We hypothesised that morphotypes would have different spatial distributions and would be associated with different habitat features based on feeding behaviour and diet. Spatially continuous sampling was conducted over a broad extent (29 km) in the Calawah River, WA (USA). Whitefish were enumerated via snorkelling in three size classes: small (10–29 cm), medium (30–49 cm), and large (≥50 cm). We identified morphotypes based on head and snout morphology: a pinocchio form that had an elongated snout and a normal form with a blunted snout. Large size classes of both morphotypes were distributed downstream of small and medium size classes, and normal whitefish were distributed downstream of pinocchio whitefish. Ordination of whitefish assemblages with nonmetric multidimensional scaling revealed that normal whitefish size classes were associated with higher gradient and depth, whereas pinocchio whitefish size classes were positively associated with pool area, distance upstream, and depth. Reach-scale generalised additive models indicated that normal whitefish relative density was associated with larger substrate size in downstream reaches (R2 = 0.64), and pinocchio whitefish were associated with greater stream depth in the reaches farther upstream (R2 = 0.87). These results suggest broad-scale spatial segregation (1–10 km), particularly between larger and more phenotypically extreme individuals. These results provide the first perspective on spatial distributions and habitat relationships of polymorphic mountain whitefish.

Bimodal Aldosterone Distribution in Low-Renin Hypertension

PubMed Central

2013-01-01

BACKGROUND In low-renin hypertension (LRH), serum aldosterone levels are higher in those subjects with primary aldosteronism and may be lower in those with non-aldosterone mineralocorticoid excess or primary renal sodium retention. We investigated the hypothesis that the frequency distribution of aldosterone in LRH is bimodal. METHODS Of the 3,532 attendees at the sixth examination cycle of the Framingham Offspring Study, 1,831 were included in this cross-sectional analysis after we excluded those with conditions or taking medications such as antihypertensive drugs that might affect renin or aldosterone. RESULTS Three hundred three subjects (17%) had untreated hypertension (SBP ≥140mm Hg or DBP ≥90mm Hg). LRH, defined as plasma renin ≤5 mU/L, was present in 93 of those 303 hypertensive subjects (31%). Aldosterone values were adjusted statistically for age, sex, and the urinary sodium/creatinine ratio. In the subjects with LRH, the adjusted aldosterone distribution was bimodal (dip test for unimodality, P = 0.008). The adjusted aldosterone distribution was unimodal in the normal subjects (P = 0.98) and in the hypertensive subjects with normal plasma renin (P = 0.94). CONCLUSIONS In this community-based sample of white subjects, those with low-renin hypertension had a bimodal adjusted aldosterone distribution. Subjects with normal-renin hypertension and subjects with normal blood pressure had unimodal adjusted aldosterone distributions. These findings suggest 2 pathophysiological variants of LRH, one that is aldosterone-dependent and one that is non-aldosterone-dependent. PMID:23757402

A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times.

PubMed

Molenaar, Dylan; Bolsinova, Maria

2017-05-01

In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set. © 2017 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Fractionation in normal tissues: the (α/β)eff concept can account for dose heterogeneity and volume effects.

PubMed

Hoffmann, Aswin L; Nahum, Alan E

2013-10-07

The simple Linear-Quadratic (LQ)-based Withers iso-effect formula (WIF) is widely used in external-beam radiotherapy to derive a new tumour dose prescription such that there is normal-tissue (NT) iso-effect when changing the fraction size and/or number. However, as conventionally applied, the WIF is invalid unless the normal-tissue response is solely determined by the tumour dose. We propose a generalized WIF (gWIF) which retains the tumour prescription dose, but replaces the intrinsic fractionation sensitivity measure (α/β) by a new concept, the normal-tissue effective fractionation sensitivity, [Formula: see text], which takes into account both the dose heterogeneity in, and the volume effect of, the late-responding normal-tissue in question. Closed-form analytical expressions for [Formula: see text] ensuring exact normal-tissue iso-effect are derived for: (i) uniform dose, and (ii) arbitrary dose distributions with volume-effect parameter n = 1 from the normal-tissue dose-volume histogram. For arbitrary dose distributions and arbitrary n, a numerical solution for [Formula: see text] exhibits a weak dependence on the number of fractions. As n is increased, [Formula: see text] increases from its intrinsic value at n = 0 (100% serial normal-tissue) to values close to or even exceeding the tumour (α/β) at n = 1 (100% parallel normal-tissue), with the highest values of [Formula: see text] corresponding to the most conformal dose distributions. Applications of this new concept to inverse planning and to highly conformal modalities are discussed, as is the effect of possible deviations from LQ behaviour at large fraction sizes.

Spatial arrangement and size distribution of normal faults, Buckskin detachment upper plate, Western Arizona

NASA Astrophysics Data System (ADS)

Laubach, S. E.; Hundley, T. H.; Hooker, J. N.; Marrett, R. A.

2018-03-01

Fault arrays typically include a wide range of fault sizes and those faults may be randomly located, clustered together, or regularly or periodically located in a rock volume. Here, we investigate size distribution and spatial arrangement of normal faults using rigorous size-scaling methods and normalized correlation count (NCC). Outcrop data from Miocene sedimentary rocks in the immediate upper plate of the regional Buckskin detachment-low angle normal-fault, have differing patterns of spatial arrangement as a function of displacement (offset). Using lower size-thresholds of 1, 0.1, 0.01, and 0.001 m, displacements range over 5 orders of magnitude and have power-law frequency distributions spanning ∼ four orders of magnitude from less than 0.001 m to more than 100 m, with exponents of -0.6 and -0.9. The largest faults with >1 m displacement have a shallower size-distribution slope and regular spacing of about 20 m. In contrast, smaller faults have steep size-distribution slopes and irregular spacing, with NCC plateau patterns indicating imposed clustering. Cluster widths are 15 m for the 0.1-m threshold, 14 m for 0.01-m, and 1 m for 0.001-m displacement threshold faults. Results demonstrate normalized correlation count effectively characterizes the spatial arrangement patterns of these faults. Our example from a high-strain fault pattern above a detachment is compatible with size and spatial organization that was influenced primarily by boundary conditions such as fault shape, mechanical unit thickness and internal stratigraphy on a range of scales rather than purely by interaction among faults during their propagation.

Parametric modelling of cost data in medical studies.

PubMed

Nixon, R M; Thompson, S G

2004-04-30

The cost of medical resources used is often recorded for each patient in clinical studies in order to inform decision-making. Although cost data are generally skewed to the right, interest is in making inferences about the population mean cost. Common methods for non-normal data, such as data transformation, assuming asymptotic normality of the sample mean or non-parametric bootstrapping, are not ideal. This paper describes possible parametric models for analysing cost data. Four example data sets are considered, which have different sample sizes and degrees of skewness. Normal, gamma, log-normal, and log-logistic distributions are fitted, together with three-parameter versions of the latter three distributions. Maximum likelihood estimates of the population mean are found; confidence intervals are derived by a parametric BC(a) bootstrap and checked by MCMC methods. Differences between model fits and inferences are explored.Skewed parametric distributions fit cost data better than the normal distribution, and should in principle be preferred for estimating the population mean cost. However for some data sets, we find that models that fit badly can give similar inferences to those that fit well. Conversely, particularly when sample sizes are not large, different parametric models that fit the data equally well can lead to substantially different inferences. We conclude that inferences are sensitive to choice of statistical model, which itself can remain uncertain unless there is enough data to model the tail of the distribution accurately. Investigating the sensitivity of conclusions to choice of model should thus be an essential component of analysing cost data in practice. Copyright 2004 John Wiley & Sons, Ltd.

Autoradiographic Distribution and Applied Pharmacological Characteristics of Dextromethorphan and Related Antitissue/Anticonvulsant Drugs and Novel Analogs

DTIC Science & Technology

1991-11-01

CHARACTERISTICS OF DEXTROMETHORPHAN AND RELATED ANTITISSUE/ANTICONVULSANT DRUGS AND NOVEL ANALOGS SUBTITLE: Receptor Binding of Dextromethorphan in Normal and...FUNDING NUMBERS Autoradiographic Distribution and Applied Pharmacologica. Characteristics of Dextromethorphan and Related Antitiss e/ Anticonvulsant...Developnent Command Fort Detrick Frederick, Maryland 21702-5012 11. SUPPLEMENTARY NOTES Subtitle: Receptor Binding of Dextromethorphan in Normal and

Normal Approximations to the Distributions of the Wilcoxon Statistics: Accurate to What "N"? Graphical Insights

ERIC Educational Resources Information Center

Bellera, Carine A.; Julien, Marilyse; Hanley, James A.

2010-01-01

The Wilcoxon statistics are usually taught as nonparametric alternatives for the 1- and 2-sample Student-"t" statistics in situations where the data appear to arise from non-normal distributions, or where sample sizes are so small that we cannot check whether they do. In the past, critical values, based on exact tail areas, were…

Confidence bounds and hypothesis tests for normal distribution coefficients of variation

Treesearch

Steve P. Verrill; Richard A. Johnson

2007-01-01

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from n-...

Are There More Gifted People Than Would Be Expected in a Normal Distribution? An Investigation of the Overabundance Hypothesis

ERIC Educational Resources Information Center

Warne, Russell T.; Godwin, Lindsey R.; Smith, Kyle V.

2013-01-01

Among some gifted education researchers, advocates, and practitioners, it is sometimes believed that there is a larger number of gifted people in the general population than would be predicted from a normal distribution (e.g., Gallagher, 2008; N. M. Robinson, Zigler, & Gallagher, 2000; Silverman, 1995, 2009), a belief that we termed the…

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

Effect of the NACA Injection Impeller on the Mixture Distribution of a Double-row Radial Aircraft Engine

NASA Technical Reports Server (NTRS)

Marble, Frank E.; Ritter, William K.; Miller, Mahlon A.

1946-01-01

For the normal range of engine power the impeller provided marked improvement over the standard spray-bar injection system. Mixture distribution at cruising was excellent, maximum cylinder temperatures were reduced about 30 degrees F, and general temperature distribution was improved. The uniform mixture distribution restored the normal response of cylinder temperature to mixture enrichment and it reduced the possibility of carburetor icing, while no serious loss in supercharger pressure rise resulted from injection of fuel near the impeller outlet. The injection impeller also furnished a convenient means of adding water to the charge mixture for internal cooling.

IS THE SUICIDE RATE A RANDOM WALK?

PubMed

Yang, Bijou; Lester, David; Lyke, Jennifer; Olsen, Robert

2015-06-01

The yearly suicide rates for the period 1933-2010 and the daily suicide numbers for 1990 and 1991 were examined for whether the distribution of difference scores (from year to year and from day to day) fitted a normal distribution, a characteristic of stochastic processes that follow a random walk. If the suicide rate were a random walk, then any disturbance to the suicide rate would have a permanent effect and national suicide prevention efforts would likely fail. The distribution of difference scores from day to day (but not the difference scores from year to year) fitted a normal distribution and, therefore, were consistent with a random walk.

Analysis of field size distributions, LACIE test sites 5029, 5033, and 5039, Anhwei Province, People's Republic of China

NASA Technical Reports Server (NTRS)

Podwysocki, M. H.

1976-01-01

A study was made of the field size distributions for LACIE test sites 5029, 5033, and 5039, People's Republic of China. Field lengths and widths were measured from LANDSAT imagery, and field area was statistically modeled. Field size parameters have log-normal or Poisson frequency distributions. These were normalized to the Gaussian distribution and theoretical population curves were made. When compared to fields in other areas of the same country measured in the previous study, field lengths and widths in the three LACIE test sites were 2 to 3 times smaller and areas were smaller by an order of magnitude.

Estimating division and death rates from CFSE data

NASA Astrophysics Data System (ADS)

de Boer, Rob J.; Perelson, Alan S.

2005-12-01

The division tracking dye, carboxyfluorescin diacetate succinimidyl ester (CFSE) is currently the most informative labeling technique for characterizing the division history of cells in the immune system. Gett and Hodgkin (Nat. Immunol. 1 (2000) 239-244) have proposed to normalize CFSE data by the 2-fold expansion that is associated with each division, and have argued that the mean of the normalized data increases linearly with time, t, with a slope reflecting the division rate p. We develop a number of mathematical models for the clonal expansion of quiescent cells after stimulation and show, within the context of these models, under which conditions this approach is valid. We compare three means of the distribution of cells over the CFSE profile at time t: the mean, [mu](t), the mean of the normalized distribution, [mu]2(t), and the mean of the normalized distribution excluding nondivided cells, .In the simplest models, which deal with homogeneous populations of cells with constant division and death rates, the normalized frequency distribution of the cells over the respective division numbers is a Poisson distribution with mean [mu]2(t)=pt, where p is the division rate. The fact that in the data these distributions seem Gaussian is therefore insufficient to establish that the times at which cells are recruited into the first division have a Gaussian variation because the Poisson distribution approaches the Gaussian distribution for large pt. Excluding nondivided cells complicates the data analysis because , and only approaches a slope p after an initial transient.In models where the first division of the quiescent cells takes longer than later divisions, all three means have an initial transient before they approach an asymptotic regime, which is the expected [mu](t)=2pt and . Such a transient markedly complicates the data analysis. After the same initial transients, the normalized cell numbers tend to decrease at a rate e-dt, where d is the death rate.Nonlinear parameter fitting of CFSE data obtained from Gett and Hodgkin to ordinary differential equation (ODE) models with first-order terms for cell proliferation and death gave poor fits to the data. The Smith-Martin model with an explicit time delay for the deterministic phase of the cell cycle performed much better. Nevertheless, the insights gained from analysis of the ODEs proved useful as we showed by generating virtual CFSE data with a simulation model, where cell cycle times were drawn from various distributions, and then computing the various mean division numbers.

Estimating and testing interactions when explanatory variables are subject to non-classical measurement error.

PubMed

Murad, Havi; Kipnis, Victor; Freedman, Laurence S

2016-10-01

Assessing interactions in linear regression models when covariates have measurement error (ME) is complex.We previously described regression calibration (RC) methods that yield consistent estimators and standard errors for interaction coefficients of normally distributed covariates having classical ME. Here we extend normal based RC (NBRC) and linear RC (LRC) methods to a non-classical ME model, and describe more efficient versions that combine estimates from the main study and internal sub-study. We apply these methods to data from the Observing Protein and Energy Nutrition (OPEN) study. Using simulations we show that (i) for normally distributed covariates efficient NBRC and LRC were nearly unbiased and performed well with sub-study size ≥200; (ii) efficient NBRC had lower MSE than efficient LRC; (iii) the naïve test for a single interaction had type I error probability close to the nominal significance level, whereas efficient NBRC and LRC were slightly anti-conservative but more powerful; (iv) for markedly non-normal covariates, efficient LRC yielded less biased estimators with smaller variance than efficient NBRC. Our simulations suggest that it is preferable to use: (i) efficient NBRC for estimating and testing interaction effects of normally distributed covariates and (ii) efficient LRC for estimating and testing interactions for markedly non-normal covariates. © The Author(s) 2013.

Understanding a Normal Distribution of Data (Part 2).

PubMed

Maltenfort, Mitchell

2016-02-01

Completing the discussion of data normality, advanced techniques for analysis of non-normal data are discussed including data transformation, Generalized Linear Modeling, and bootstrapping. Relative strengths and weaknesses of each technique are helpful in choosing a strategy, but help from a statistician is usually necessary to analyze non-normal data using these methods.

New approach application of data transformation in mean centering of ratio spectra method

NASA Astrophysics Data System (ADS)

Issa, Mahmoud M.; Nejem, R.'afat M.; Van Staden, Raluca Ioana Stefan; Aboul-Enein, Hassan Y.

2015-05-01

Most of mean centering (MCR) methods are designed to be used with data sets whose values have a normal or nearly normal distribution. The errors associated with the values are also assumed to be independent and random. If the data are skewed, the results obtained may be doubtful. Most of the time, it was assumed a normal distribution and if a confidence interval includes a negative value, it was cut off at zero. However, it is possible to transform the data so that at least an approximately normal distribution is attained. Taking the logarithm of each data point is one transformation frequently used. As a result, the geometric mean is deliberated a better measure of central tendency than the arithmetic mean. The developed MCR method using the geometric mean has been successfully applied to the analysis of a ternary mixture of aspirin (ASP), atorvastatin (ATOR) and clopidogrel (CLOP) as a model. The results obtained were statistically compared with reported HPLC method.

Distribution of erlotinib in rash and normal skin in cancer patients receiving erlotinib visualized by matrix assisted laser desorption/ionization mass spectrometry imaging.

PubMed

Nishimura, Meiko; Hayashi, Mitsuhiro; Mizutani, Yu; Takenaka, Kei; Imamura, Yoshinori; Chayahara, Naoko; Toyoda, Masanori; Kiyota, Naomi; Mukohara, Toru; Aikawa, Hiroaki; Fujiwara, Yasuhiro; Hamada, Akinobu; Minami, Hironobu

2018-04-06

The development of skin rashes is the most common adverse event observed in cancer patients treated with epidermal growth factor receptor-tyrosine kinase inhibitors such as erlotinib. However, the pharmacological evidence has not been fully revealed. Erlotinib distribution in the rashes was more heterogeneous than that in the normal skin, and the rashes contained statistically higher concentrations of erlotinib than adjacent normal skin in the superficial skin layer (229 ± 192 vs. 120 ± 103 ions/mm 2 ; P = 0.009 in paired t -test). LC-MS/MS confirmed that the concentration of erlotinib in the skin rashes was higher than that in normal skin in the superficial skin layer (1946 ± 1258 vs. 1174 ± 662 ng/cm 3 ; P = 0.028 in paired t -test). The results of MALDI-MSI and LC-MS/MS were well correlated (coefficient of correlation 0.879, P < 0.0001). Focal distribution of erlotinib in the skin tissue was visualized using non-labeled MALDI-MSI. Erlotinib concentration in the superficial layer of the skin rashes was higher than that in the adjacent normal skin. We examined patients with advanced pancreatic cancer who developed skin rashes after treatment with erlotinib and gemcitabine. We biopsied both the rash and adjacent normal skin tissues, and visualized and compared the distribution of erlotinib within the skin using matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI). The tissue concentration of erlotinib was also measured by liquid chromatography-tandem mass spectrometry (LC-MS/MS) with laser microdissection.

Distribution of erlotinib in rash and normal skin in cancer patients receiving erlotinib visualized by matrix assisted laser desorption/ionization mass spectrometry imaging

PubMed Central

Mizutani, Yu; Takenaka, Kei; Imamura, Yoshinori; Chayahara, Naoko; Toyoda, Masanori; Kiyota, Naomi; Mukohara, Toru; Aikawa, Hiroaki; Fujiwara, Yasuhiro; Hamada, Akinobu; Minami, Hironobu

2018-01-01

Background The development of skin rashes is the most common adverse event observed in cancer patients treated with epidermal growth factor receptor-tyrosine kinase inhibitors such as erlotinib. However, the pharmacological evidence has not been fully revealed. Results Erlotinib distribution in the rashes was more heterogeneous than that in the normal skin, and the rashes contained statistically higher concentrations of erlotinib than adjacent normal skin in the superficial skin layer (229 ± 192 vs. 120 ± 103 ions/mm2; P = 0.009 in paired t-test). LC-MS/MS confirmed that the concentration of erlotinib in the skin rashes was higher than that in normal skin in the superficial skin layer (1946 ± 1258 vs. 1174 ± 662 ng/cm3; P = 0.028 in paired t-test). The results of MALDI-MSI and LC-MS/MS were well correlated (coefficient of correlation 0.879, P < 0.0001). Conclusions Focal distribution of erlotinib in the skin tissue was visualized using non-labeled MALDI-MSI. Erlotinib concentration in the superficial layer of the skin rashes was higher than that in the adjacent normal skin. Methods We examined patients with advanced pancreatic cancer who developed skin rashes after treatment with erlotinib and gemcitabine. We biopsied both the rash and adjacent normal skin tissues, and visualized and compared the distribution of erlotinib within the skin using matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI). The tissue concentration of erlotinib was also measured by liquid chromatography-tandem mass spectrometry (LC–MS/MS) with laser microdissection. PMID:29719624

A time-frequency approach for the analysis of normal and arrhythmia cardiac signals.

PubMed

Mahmoud, Seedahmed S; Fang, Qiang; Davidović, Dragomir M; Cosic, Irena

2006-01-01

Previously, electrocardiogram (ECG) signals have been analyzed in either a time-indexed or spectral form. The reality, is that the ECG and all other biological signals belong to the family of multicomponent nonstationary signals. Due to this reason, the use of time-frequency analysis can be unavoidable for these signals. The Husimi and Wigner distributions are normally used in quantum mechanics for phase space representations of the wavefunction. In this paper, we introduce the Husimi distribution (HD) to analyze the normal and abnormal ECG signals in time-frequency domain. The abnormal cardiac signal was taken from a patient with supraventricular arrhythmia. Simulation results show that the HD has a good performance in the analysis of the ECG signals comparing with the Wigner-Ville distribution (WVD).

Diet-induced obesity, exogenous leptin-, and MADB106 tumor cell challenge affect tissue leukocyte distribution and serum levels of cytokines in F344 rats.

PubMed

Behrendt, Patrick; Buchenauer, Tobias; Horn, Rüdiger; Brabant, Georg; Jacobs, Roland; Bode, Felix; Stephan, Michael; Nave, Heike

2010-08-01

The adipocyte-derived catabolic protein leptin alters cell-mediated immunity and cytokine crosstalk. This may provide new insights into the altered immune response, seen in obese individuals. Therefore, we determined the tissue distribution of immune cells in diet-induced obese (dio) and normal weight F344 rats challenged with MADB106 tumor cells or leptin. Immune cell distribution in blood (by FACS analysis) and tissues (NK cells in spleen and liver, immunohistologically) as well as pro-inflammatory cytokines (IL-6, TNF-α; by flow cytometry) were investigated in 28 normal weight and 28 dio rats (n = 4-6/group). Pro-inflammatory cytokines were increased 3-fold for IL-6 and 7-fold for TNF-α in obese animals. Higher numbers of blood monocytes and NK cells were found in obese as compared to normal weight animals. In dio rats challenged with leptin and MADB106 tumor cells, monocyte numbers were decreased as compared to the obese control animals. Immunohistochemistry revealed an altered NK cell distribution in a compartment-, treatment-, and bodyweight-specific manner. In conclusion, our data reveal a distinct distribution pattern of monocytes and NK cells in dio rats as compared to normal weight littermates and an additional modulatory effect of a leptin- and MADB106 tumor cell challenge.

Wind Power Forecasting Error Distributions over Multiple Timescales: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hodge, B. M.; Milligan, M.

2011-03-01

In this paper, we examine the shape of the persistence model error distribution for ten different wind plants in the ERCOT system over multiple timescales. Comparisons are made between the experimental distribution shape and that of the normal distribution.

The distribution of emission-line galaxies in selected areas of the sky

NASA Astrophysics Data System (ADS)

Moody, J. Ward

1988-11-01

The author discusses the spatial distribution of emission-line galaxies (ELGs) relative to normal galaxies in several areas of the sky. Current evidence supports the notion that ELGs trace a low-density population in all the surveyed areas with the possible exception of the CfA "Slice of the Universe" survey. Based on this and other survey data in the north galactic cap, it is suggested that the ELGs inside the Bootes void may actually define the edge of a totally empty volume within an underdense distribution of normal galaxies.

The distribution of emission-line galaxies in selected areas of the sky

NASA Technical Reports Server (NTRS)

Moody, J. Ward

1988-01-01

The spatial distribution of emission-line galaxies (ELGs) relative to normal galaxies in several areas of the sky is discussed. Current evidence supports the notion that ELGs trace a low-density population in all the surveyed areas with the possible exception of the CfA 'Slice of the Universe' survey. Based on this and other survey data in the north galactic cap, it is suggested that the ELGs inside the Bootes void may actually define the edge of a totally empty volume within an underdense distribution of normal galaxies.

Elastin distribution in the normal uterus, uterine leiomyomas, adenomyosis and adenomyomas: a comparison.

PubMed

Zheng, Wei-Qiang; Ma, Rong; Zheng, Jian-Ming; Gong, Zhi-Jing

2006-04-01

To describe the histologic distribution of elastin in the nonpregnant human uterus, uterine leiomyomas, adenomyosis and adenomyomas. Uteri were obtained from women undergoing hysterectomy for benign conditions, including 26 cases of uterine leiomyomas, 24 cases of adenomyosis, 18 adenomyomas and 6 cases of autopsy specimens. Specific histochemical staining techniques were employed in order to demonstrate the distribution of elastin. The distribution of elastin components in the uterus was markedly uneven and showed a decreasing gradient from outer to inner myometrium. No elastin was present within leiomyomas, adenomyomas or adenomyosis. The distribution of elastin may help explain the normal function of the myometrium in labor. It implies that the uneven distribution of elastin components and absence of elastin within leiomyomas, adenomyomas and adenomyosis could be of some clinical significance. The altered elastin distribution in disease states may help explain such symptoms as dysmenorrhea in uterine endometriosis.

Energetics and Birth Rates of Supernova Remnants in the Large Magellanic Cloud

NASA Astrophysics Data System (ADS)

Leahy, D. A.

2017-03-01

Published X-ray emission properties for a sample of 50 supernova remnants (SNRs) in the Large Magellanic Cloud (LMC) are used as input for SNR evolution modeling calculations. The forward shock emission is modeled to obtain the initial explosion energy, age, and circumstellar medium density for each SNR in the sample. The resulting age distribution yields a SNR birthrate of 1/(500 yr) for the LMC. The explosion energy distribution is well fit by a log-normal distribution, with a most-probable explosion energy of 0.5× {10}51 erg, with a 1σ dispersion by a factor of 3 in energy. The circumstellar medium density distribution is broader than the explosion energy distribution, with a most-probable density of ˜0.1 cm-3. The shape of the density distribution can be fit with a log-normal distribution, with incompleteness at high density caused by the shorter evolution times of SNRs.

Transponder-aided joint calibration and synchronization compensation for distributed radar systems.

PubMed

Wang, Wen-Qin

2015-01-01

High-precision radiometric calibration and synchronization compensation must be provided for distributed radar system due to separate transmitters and receivers. This paper proposes a transponder-aided joint radiometric calibration, motion compensation and synchronization for distributed radar remote sensing. As the transponder signal can be separated from the normal radar returns, it is used to calibrate the distributed radar for radiometry. Meanwhile, the distributed radar motion compensation and synchronization compensation algorithms are presented by utilizing the transponder signals. This method requires no hardware modifications to both the normal radar transmitter and receiver and no change to the operating pulse repetition frequency (PRF). The distributed radar radiometric calibration and synchronization compensation require only one transponder, but the motion compensation requires six transponders because there are six independent variables in the distributed radar geometry. Furthermore, a maximum likelihood method is used to estimate the transponder signal parameters. The proposed methods are verified by simulation results.

A new stochastic algorithm for inversion of dust aerosol size distribution

NASA Astrophysics Data System (ADS)

Wang, Li; Li, Feng; Yang, Ma-ying

2015-08-01

Dust aerosol size distribution is an important source of information about atmospheric aerosols, and it can be determined from multiwavelength extinction measurements. This paper describes a stochastic inverse technique based on artificial bee colony (ABC) algorithm to invert the dust aerosol size distribution by light extinction method. The direct problems for the size distribution of water drop and dust particle, which are the main elements of atmospheric aerosols, are solved by the Mie theory and the Lambert-Beer Law in multispectral region. And then, the parameters of three widely used functions, i.e. the log normal distribution (L-N), the Junge distribution (J-J), and the normal distribution (N-N), which can provide the most useful representation of aerosol size distributions, are inversed by the ABC algorithm in the dependent model. Numerical results show that the ABC algorithm can be successfully applied to recover the aerosol size distribution with high feasibility and reliability even in the presence of random noise.

Prediction of the filtrate particle size distribution from the pore size distribution in membrane filtration: Numerical correlations from computer simulations

NASA Astrophysics Data System (ADS)

Marrufo-Hernández, Norma Alejandra; Hernández-Guerrero, Maribel; Nápoles-Duarte, José Manuel; Palomares-Báez, Juan Pedro; Chávez-Rojo, Marco Antonio

2018-03-01

We present a computational model that describes the diffusion of a hard spheres colloidal fluid through a membrane. The membrane matrix is modeled as a series of flat parallel planes with circular pores of different sizes and random spatial distribution. This model was employed to determine how the size distribution of the colloidal filtrate depends on the size distributions of both, the particles in the feed and the pores of the membrane, as well as to describe the filtration kinetics. A Brownian dynamics simulation study considering normal distributions was developed in order to determine empirical correlations between the parameters that characterize these distributions. The model can also be extended to other distributions such as log-normal. This study could, therefore, facilitate the selection of membranes for industrial or scientific filtration processes once the size distribution of the feed is known and the expected characteristics in the filtrate have been defined.

Inferring local competition intensity from patch size distributions: a test using biological soil crusts

USGS Publications Warehouse

Bowker, Matthew A.; Maestre, Fernando T.

2012-01-01

Dryland vegetation is inherently patchy. This patchiness goes on to impact ecology, hydrology, and biogeochemistry. Recently, researchers have proposed that dryland vegetation patch sizes follow a power law which is due to local plant facilitation. It is unknown what patch size distribution prevails when competition predominates over facilitation, or if such a pattern could be used to detect competition. We investigated this question in an alternative vegetation type, mosses and lichens of biological soil crusts, which exhibit a smaller scale patch-interpatch configuration. This micro-vegetation is characterized by competition for space. We proposed that multiplicative effects of genetics, environment and competition should result in a log-normal patch size distribution. When testing the prevalence of log-normal versus power law patch size distributions, we found that the log-normal was the better distribution in 53% of cases and a reasonable fit in 83%. In contrast, the power law was better in 39% of cases, and in 8% of instances both distributions fit equally well. We further hypothesized that the log-normal distribution parameters would be predictably influenced by competition strength. There was qualitative agreement between one of the distribution's parameters (μ) and a novel intransitive (lacking a 'best' competitor) competition index, suggesting that as intransitivity increases, patch sizes decrease. The correlation of μ with other competition indicators based on spatial segregation of species (the C-score) depended on aridity. In less arid sites, μ was negatively correlated with the C-score (suggesting smaller patches under stronger competition), while positive correlations (suggesting larger patches under stronger competition) were observed at more arid sites. We propose that this is due to an increasing prevalence of competition transitivity as aridity increases. These findings broaden the emerging theory surrounding dryland patch size distributions and, with refinement, may help us infer cryptic ecological processes from easily observed spatial patterns in the field.

Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

PubMed

Abe, Sumiyoshi

2002-10-01

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.

Distribution of the anticancer drugs doxorubicin, mitoxantrone and topotecan in tumors and normal tissues.

PubMed

Patel, Krupa J; Trédan, Olivier; Tannock, Ian F

2013-07-01

Pharmacokinetic analyses estimate the mean concentration of drug within a given tissue as a function of time, but do not give information about the spatial distribution of drugs within that tissue. Here, we compare the time-dependent spatial distribution of three anticancer drugs within tumors, heart, kidney, liver and brain. Mice bearing various xenografts were treated with doxorubicin, mitoxantrone or topotecan. At various times after injection, tumors and samples of heart, kidney, liver and brain were excised. Within solid tumors, the distribution of doxorubicin, mitoxantrone and topotecan was limited to perivascular regions at 10 min after administration and the distance from blood vessels at which drug intensity fell to half was ~25-75 μm. Although drug distribution improved after 3 and 24 h, there remained a significant decrease in drug fluorescence with increasing distance from tumor blood vessels. Drug distribution was relatively uniform in the heart, kidney and liver with substantially greater perivascular drug uptake than in tumors. There was significantly higher total drug fluorescence in the liver than in tumors after 10 min, 3 and 24 h. Little to no drug fluorescence was observed in the brain. There are marked differences in the spatial distributions of three anticancer drugs within tumor tissue and normal tissues over time, with greater exposure to most normal tissues and limited drug distribution to many cells in tumors. Studies of the spatial distribution of drugs are required to complement pharmacokinetic data in order to better understand and predict drug effects and toxicities.

The Weight of Euro Coins: Its Distribution Might Not Be as Normal as You Would Expect

ERIC Educational Resources Information Center

Shkedy, Ziv; Aerts, Marc; Callaert, Herman

2006-01-01

Classical regression models, ANOVA models and linear mixed models are just three examples (out of many) in which the normal distribution of the response is an essential assumption of the model. In this paper we use a dataset of 2000 euro coins containing information (up to the milligram) about the weight of each coin, to illustrate that the…

The formulation and estimation of a spatial skew-normal generalized ordered-response model.

DOT National Transportation Integrated Search

2016-06-01

This paper proposes a new spatial generalized ordered response model with skew-normal kernel error terms and an : associated estimation method. It contributes to the spatial analysis field by allowing a flexible and parametric skew-normal : distribut...

Verification of echo amplitude envelope analysis method in skin tissues for quantitative follow-up of healing ulcers

NASA Astrophysics Data System (ADS)

Omura, Masaaki; Yoshida, Kenji; Akita, Shinsuke; Yamaguchi, Tadashi

2018-07-01

We aim to develop an ultrasonic tissue characterization method for the follow-up of healing ulcers by diagnosing collagen fibers properties. In this paper, we demonstrated a computer simulation with simulation phantoms reflecting irregularly distributed collagen fibers to evaluate the relationship between physical properties, such as number density and periodicity, and the estimated characteristics of the echo amplitude envelope using the homodyned-K distribution. Moreover, the consistency between echo signal characteristics and the structures of ex vivo human tissues was verified from the measured data of normal skin and nonhealed ulcers. In the simulation study, speckle or coherent signal characteristics are identified as periodically or uniformly distributed collagen fibers with high number density and high periodicity. This result shows the effectiveness of the analysis using the homodyned-K distribution for tissues with complicated structures. Normal skin analysis results are characterized as including speckle or low-coherence signal components, and a nonhealed ulcer is different from normal skin with respect to the physical properties of collagen fibers.

Thinking positively: The genetics of high intelligence

PubMed Central

Shakeshaft, Nicholas G.; Trzaskowski, Maciej; McMillan, Andrew; Krapohl, Eva; Simpson, Michael A.; Reichenberg, Avi; Cederlöf, Martin; Larsson, Henrik; Lichtenstein, Paul; Plomin, Robert

2015-01-01

High intelligence (general cognitive ability) is fundamental to the human capital that drives societies in the information age. Understanding the origins of this intellectual capital is important for government policy, for neuroscience, and for genetics. For genetics, a key question is whether the genetic causes of high intelligence are qualitatively or quantitatively different from the normal distribution of intelligence. We report results from a sibling and twin study of high intelligence and its links with the normal distribution. We identified 360,000 sibling pairs and 9000 twin pairs from 3 million 18-year-old males with cognitive assessments administered as part of conscription to military service in Sweden between 1968 and 2010. We found that high intelligence is familial, heritable, and caused by the same genetic and environmental factors responsible for the normal distribution of intelligence. High intelligence is a good candidate for “positive genetics” — going beyond the negative effects of DNA sequence variation on disease and disorders to consider the positive end of the distribution of genetic effects. PMID:25593376

Lithographic stochastics: beyond 3σ

NASA Astrophysics Data System (ADS)

Bristol, Robert L.; Krysak, Marie E.

2017-04-01

As lithography tools continue their progress in both numerical aperture and wavelength in pursuit of Moore's law, we have reached the point where the number of features printed in a single pass can now easily surpass one trillion. Statistically, one should not be surprised to see some members of such a population exhibit fluctuations as great as 7σ. But what do these fluctuations look like? We consider the problem in terms of variations in the effective local resist sensitivity caused by feature-to-feature differences in absorbed photons and resist component counts, modeling these as a normal distribution. As the CD versus dose curve is generally nonlinear over large ranges, the normal distribution of the local effective sensitivity then maps to a nonnormal distribution in CD. For the case of individual vias printed near the resolution limit, it results in many more undersized or completely closed vias than one would expect from a normal distribution of the CDs. We show examples of this behavior from both EUV exposures in the fab and ebeam exposures in the lab.

Black-Litterman model on non-normal stock return (Case study four banks at LQ-45 stock index)

NASA Astrophysics Data System (ADS)

Mahrivandi, Rizki; Noviyanti, Lienda; Setyanto, Gatot Riwi

2017-03-01

The formation of the optimal portfolio is a method that can help investors to minimize risks and optimize profitability. One model for the optimal portfolio is a Black-Litterman (BL) model. BL model can incorporate an element of historical data and the views of investors to form a new prediction about the return of the portfolio as a basis for preparing the asset weighting models. BL model has two fundamental problems, the assumption of normality and estimation parameters on the market Bayesian prior framework that does not from a normal distribution. This study provides an alternative solution where the modelling of the BL model stock returns and investor views from non-normal distribution.

Comparative pharmacokinetics and tissue distribution profiles of lignan components in normal and hepatic fibrosis rats after oral administration of Fuzheng Huayu recipe.

PubMed

Yang, Tao; Liu, Shan; Zheng, Tian-Hui; Tao, Yan-Yan; Liu, Cheng-Hai

2015-05-26

Fuzheng Huayu recipe (FZHY) is formulated on the basis of Chinese medicine theory in treating liver fibrosis. To illuminate the influence of the pathological state of liver fibrosis on the pharmacokinetics and tissue distribution profiles of lignan components from FZHY. Male Wistar rats were randomly divided into normal group and Hepatic fibrosis group (induced by dimethylnitrosamine). Six lignan components were detected and quantified by ultrahigh performance liquid chromatography-tandem mass spectrometry(UHPLC-MS/MS)in the plasma and tissue of normal and hepatic fibrosis rats. A rapid, sensitive and convenient UHPLC-MS/MS method has been developed for the simultaneous determination of six lignan components in different rat biological samples successfully. After oral administration of FZHY at a dose of 15g/kg, the pharmacokinetic behaviors of schizandrin A (SIA), schizandrin B (SIB), schizandrin C (SIC), schisandrol A (SOA), Schisandrol B (SOB) and schisantherin A (STA) have been significantly changed in hepatic fibrosis rats compared with the normal rats, and their AUC(0-t) values were increased by 235.09%, 388.44%, 223.30%, 669.30%, 295.08% and 267.63% orderly (P<0.05). Tissue distribution results showed the amount of SIA, SIB, SOA and SOB were significant increased in heart, lung, spleen and kidney of hepatic fibrosis rats compared with normal rats at most of the time point (P<0.05). Meanwhile, the result also reveals that the hepatic fibrosis could delay the peak time of lignans in liver. The results proved that the established UHPLC-MS/MS method could be applied to the comparative study on pharmacokinetics and tissue distribution of lignan components in normal and hepatic fibrosis rats. The hepatic fibrosis could alter the pharmacokinetics and tissue distribution properties of lignan components in rats after administration of FZHY. The results might be helpful for guide the clinical application of this medicine. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Assessing differential expression in two-color microarrays: a resampling-based empirical Bayes approach.

PubMed

Li, Dongmei; Le Pape, Marc A; Parikh, Nisha I; Chen, Will X; Dye, Timothy D

2013-01-01

Microarrays are widely used for examining differential gene expression, identifying single nucleotide polymorphisms, and detecting methylation loci. Multiple testing methods in microarray data analysis aim at controlling both Type I and Type II error rates; however, real microarray data do not always fit their distribution assumptions. Smyth's ubiquitous parametric method, for example, inadequately accommodates violations of normality assumptions, resulting in inflated Type I error rates. The Significance Analysis of Microarrays, another widely used microarray data analysis method, is based on a permutation test and is robust to non-normally distributed data; however, the Significance Analysis of Microarrays method fold change criteria are problematic, and can critically alter the conclusion of a study, as a result of compositional changes of the control data set in the analysis. We propose a novel approach, combining resampling with empirical Bayes methods: the Resampling-based empirical Bayes Methods. This approach not only reduces false discovery rates for non-normally distributed microarray data, but it is also impervious to fold change threshold since no control data set selection is needed. Through simulation studies, sensitivities, specificities, total rejections, and false discovery rates are compared across the Smyth's parametric method, the Significance Analysis of Microarrays, and the Resampling-based empirical Bayes Methods. Differences in false discovery rates controls between each approach are illustrated through a preterm delivery methylation study. The results show that the Resampling-based empirical Bayes Methods offer significantly higher specificity and lower false discovery rates compared to Smyth's parametric method when data are not normally distributed. The Resampling-based empirical Bayes Methods also offers higher statistical power than the Significance Analysis of Microarrays method when the proportion of significantly differentially expressed genes is large for both normally and non-normally distributed data. Finally, the Resampling-based empirical Bayes Methods are generalizable to next generation sequencing RNA-seq data analysis.

Problems with Using the Normal Distribution – and Ways to Improve Quality and Efficiency of Data Analysis

PubMed Central

Limpert, Eckhard; Stahel, Werner A.

2011-01-01

Background The Gaussian or normal distribution is the most established model to characterize quantitative variation of original data. Accordingly, data are summarized using the arithmetic mean and the standard deviation, by ± SD, or with the standard error of the mean, ± SEM. This, together with corresponding bars in graphical displays has become the standard to characterize variation. Methodology/Principal Findings Here we question the adequacy of this characterization, and of the model. The published literature provides numerous examples for which such descriptions appear inappropriate because, based on the “95% range check”, their distributions are obviously skewed. In these cases, the symmetric characterization is a poor description and may trigger wrong conclusions. To solve the problem, it is enlightening to regard causes of variation. Multiplicative causes are by far more important than additive ones, in general, and benefit from a multiplicative (or log-) normal approach. Fortunately, quite similar to the normal, the log-normal distribution can now be handled easily and characterized at the level of the original data with the help of both, a new sign, x/, times-divide, and notation. Analogous to ± SD, it connects the multiplicative (or geometric) mean * and the multiplicative standard deviation s* in the form * x/s*, that is advantageous and recommended. Conclusions/Significance The corresponding shift from the symmetric to the asymmetric view will substantially increase both, recognition of data distributions, and interpretation quality. It will allow for savings in sample size that can be considerable. Moreover, this is in line with ethical responsibility. Adequate models will improve concepts and theories, and provide deeper insight into science and life. PMID:21779325

Problems with using the normal distribution--and ways to improve quality and efficiency of data analysis.

PubMed

Limpert, Eckhard; Stahel, Werner A

2011-01-01

The gaussian or normal distribution is the most established model to characterize quantitative variation of original data. Accordingly, data are summarized using the arithmetic mean and the standard deviation, by mean ± SD, or with the standard error of the mean, mean ± SEM. This, together with corresponding bars in graphical displays has become the standard to characterize variation. Here we question the adequacy of this characterization, and of the model. The published literature provides numerous examples for which such descriptions appear inappropriate because, based on the "95% range check", their distributions are obviously skewed. In these cases, the symmetric characterization is a poor description and may trigger wrong conclusions. To solve the problem, it is enlightening to regard causes of variation. Multiplicative causes are by far more important than additive ones, in general, and benefit from a multiplicative (or log-) normal approach. Fortunately, quite similar to the normal, the log-normal distribution can now be handled easily and characterized at the level of the original data with the help of both, a new sign, x/, times-divide, and notation. Analogous to mean ± SD, it connects the multiplicative (or geometric) mean mean * and the multiplicative standard deviation s* in the form mean * x/s*, that is advantageous and recommended. The corresponding shift from the symmetric to the asymmetric view will substantially increase both, recognition of data distributions, and interpretation quality. It will allow for savings in sample size that can be considerable. Moreover, this is in line with ethical responsibility. Adequate models will improve concepts and theories, and provide deeper insight into science and life.

Normality of raw data in general linear models: The most widespread myth in statistics

USGS Publications Warehouse

Kery, Marc; Hatfield, Jeff S.

2003-01-01

In years of statistical consulting for ecologists and wildlife biologists, by far the most common misconception we have come across has been the one about normality in general linear models. These comprise a very large part of the statistical models used in ecology and include t tests, simple and multiple linear regression, polynomial regression, and analysis of variance (ANOVA) and covariance (ANCOVA). There is a widely held belief that the normality assumption pertains to the raw data rather than to the model residuals. We suspect that this error may also occur in countless published studies, whenever the normality assumption is tested prior to analysis. This may lead to the use of nonparametric alternatives (if there are any), when parametric tests would indeed be appropriate, or to use of transformations of raw data, which may introduce hidden assumptions such as multiplicative effects on the natural scale in the case of log-transformed data. Our aim here is to dispel this myth. We very briefly describe relevant theory for two cases of general linear models to show that the residuals need to be normally distributed if tests requiring normality are to be used, such as t and F tests. We then give two examples demonstrating that the distribution of the response variable may be nonnormal, and yet the residuals are well behaved. We do not go into the issue of how to test normality; instead we display the distributions of response variables and residuals graphically.

Therapeutic analysis of high-dose-rate {sup 192}Ir vaginal cuff brachytherapy for endometrial cancer using a cylindrical target volume model and varied cancer cell distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hualin, E-mail: hualin.zhang@northwestern.edu; Donnelly, Eric D.; Strauss, Jonathan B.

Purpose: To evaluate high-dose-rate (HDR) vaginal cuff brachytherapy (VCBT) in the treatment of endometrial cancer in a cylindrical target volume with either a varied or a constant cancer cell distributions using the linear quadratic (LQ) model. Methods: A Monte Carlo (MC) technique was used to calculate the 3D dose distribution of HDR VCBT over a variety of cylinder diameters and treatment lengths. A treatment planning system (TPS) was used to make plans for the various cylinder diameters, treatment lengths, and prescriptions using the clinical protocol. The dwell times obtained from the TPS were fed into MC. The LQ model wasmore » used to evaluate the therapeutic outcome of two brachytherapy regimens prescribed either at 0.5 cm depth (5.5 Gy × 4 fractions) or at the vaginal mucosal surface (8.8 Gy × 4 fractions) for the treatment of endometrial cancer. An experimentally determined endometrial cancer cell distribution, which showed a varied and resembled a half-Gaussian distribution, was used in radiobiology modeling. The equivalent uniform dose (EUD) to cancer cells was calculated for each treatment scenario. The therapeutic ratio (TR) was defined by comparing VCBT with a uniform dose radiotherapy plan in term of normal cell survival at the same level of cancer cell killing. Calculations of clinical impact were run twice assuming two different types of cancer cell density distributions in the cylindrical target volume: (1) a half-Gaussian or (2) a uniform distribution. Results: EUDs were weakly dependent on cylinder size, treatment length, and the prescription depth, but strongly dependent on the cancer cell distribution. TRs were strongly dependent on the cylinder size, treatment length, types of the cancer cell distributions, and the sensitivity of normal tissue. With a half-Gaussian distribution of cancer cells which populated at the vaginal mucosa the most, the EUDs were between 6.9 Gy × 4 and 7.8 Gy × 4, the TRs were in the range from (5.0){sup 4} to (13.4){sup 4} for the radiosensitive normal tissue depending on the cylinder size, treatment lengths, prescription depth, and dose as well. However, for a uniform cancer cell distribution, the EUDs were between 6.3 Gy × 4 and 7.1 Gy × 4, and the TRs were found to be between (1.4){sup 4} and (1.7){sup 4}. For the uniformly interspersed cancer and radio-resistant normal cells, the TRs were less than 1. The two VCBT prescription regimens were found to be equivalent in terms of EUDs and TRs. Conclusions: HDR VCBT strongly favors cylindrical target volume with the cancer cell distribution following its dosimetric trend. Assuming a half-Gaussian distribution of cancer cells, the HDR VCBT provides a considerable radiobiological advantage over the external beam radiotherapy (EBRT) in terms of sparing more normal tissues while maintaining the same level of cancer cell killing. But for the uniform cancer cell distribution and radio-resistant normal tissue, the radiobiology outcome of the HDR VCBT does not show an advantage over the EBRT. This study strongly suggests that radiation therapy design should consider the cancer cell distribution inside the target volume in addition to the shape of target.« less

The Distribution of the Sum of Signed Ranks

ERIC Educational Resources Information Center

Albright, Brian

2012-01-01

We describe the calculation of the distribution of the sum of signed ranks and develop an exact recursive algorithm for the distribution as well as an approximation of the distribution using the normal. The results have applications to the non-parametric Wilcoxon signed-rank test.

Active control of impulsive noise with symmetric α-stable distribution based on an improved step-size normalized adaptive algorithm

NASA Astrophysics Data System (ADS)

Zhou, Yali; Zhang, Qizhi; Yin, Yixin

2015-05-01

In this paper, active control of impulsive noise with symmetric α-stable (SαS) distribution is studied. A general step-size normalized filtered-x Least Mean Square (FxLMS) algorithm is developed based on the analysis of existing algorithms, and the Gaussian distribution function is used to normalize the step size. Compared with existing algorithms, the proposed algorithm needs neither the parameter selection and thresholds estimation nor the process of cost function selection and complex gradient computation. Computer simulations have been carried out to suggest that the proposed algorithm is effective for attenuating SαS impulsive noise, and then the proposed algorithm has been implemented in an experimental ANC system. Experimental results show that the proposed scheme has good performance for SαS impulsive noise attenuation.

Principal Component Analysis for Normal-Distribution-Valued Symbolic Data.

PubMed

Wang, Huiwen; Chen, Meiling; Shi, Xiaojun; Li, Nan

2016-02-01

This paper puts forward a new approach to principal component analysis (PCA) for normal-distribution-valued symbolic data, which has a vast potential of applications in the economic and management field. We derive a full set of numerical characteristics and variance-covariance structure for such data, which forms the foundation for our analytical PCA approach. Our approach is able to use all of the variance information in the original data than the prevailing representative-type approach in the literature which only uses centers, vertices, etc. The paper also provides an accurate approach to constructing the observations in a PC space based on the linear additivity property of normal distribution. The effectiveness of the proposed method is illustrated by simulated numerical experiments. At last, our method is applied to explain the puzzle of risk-return tradeoff in China's stock market.

Meta-analysis of prediction model performance across multiple studies: Which scale helps ensure between-study normality for the C-statistic and calibration measures?

PubMed

Snell, Kym Ie; Ensor, Joie; Debray, Thomas Pa; Moons, Karel Gm; Riley, Richard D

2017-01-01

If individual participant data are available from multiple studies or clusters, then a prediction model can be externally validated multiple times. This allows the model's discrimination and calibration performance to be examined across different settings. Random-effects meta-analysis can then be used to quantify overall (average) performance and heterogeneity in performance. This typically assumes a normal distribution of 'true' performance across studies. We conducted a simulation study to examine this normality assumption for various performance measures relating to a logistic regression prediction model. We simulated data across multiple studies with varying degrees of variability in baseline risk or predictor effects and then evaluated the shape of the between-study distribution in the C-statistic, calibration slope, calibration-in-the-large, and E/O statistic, and possible transformations thereof. We found that a normal between-study distribution was usually reasonable for the calibration slope and calibration-in-the-large; however, the distributions of the C-statistic and E/O were often skewed across studies, particularly in settings with large variability in the predictor effects. Normality was vastly improved when using the logit transformation for the C-statistic and the log transformation for E/O, and therefore we recommend these scales to be used for meta-analysis. An illustrated example is given using a random-effects meta-analysis of the performance of QRISK2 across 25 general practices.

FREQUENCY DISTRIBUTIONS OF 90SR AND 137CS CONCENTRATIONS IN AN ECOSYSTEM OF THE 'RED FOREST' AREA IN THE CHERNOBYL EXCLUSION ZONE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farfan, E.; Jannik, T.; Caldwell, E.

2011-10-01

In the most highly contaminated region of the Chernobyl Exclusion Zone: the 'Red Forest' site, the accumulation of the major dose-affecting radionuclides ({sup 90}Sr and {sup 137}Cs) within the components of an ecological system encompassing 3,000 m{sup 2} were characterized. The sampled components included soils (top 0-10 cm depth), Molina caerulea (blue moor grass), Camponotus vagus (carpenter ants) and Pelobates fuscus (spade-footed toad). In a comparison among the components of this ecosystem, the {sup 90}Sr and {sup 137}Cs concentrations measured in 40 separate grids exhibited significant differences, while the frequency distribution of the values were close to a logarithmically normalmore » leptokurtic distribution with a significant right-side skew. While it is important to identify localized areas of high contamination or 'hot spots,' including these values in the arithmetic mean may overestimate the exposure risk. In component sample sets that exhibited logarithmically normal distribution, the geometrical mean more accurately characterizes a site. Ideally, risk assessment is most confidently achieved when the arithmetic and geometrical means are most similar, meaning the distribution approaches normal. Through bioaccumulation, the highest concentrations of {sup 90}Sr and {sup 137}Cs were measured in the blue moor grass and spade-footed toad. These components also possessed distribution parameters that shifted toward a normal distribution.« less

Probability distribution functions for unit hydrographs with optimization using genetic algorithm

NASA Astrophysics Data System (ADS)

Ghorbani, Mohammad Ali; Singh, Vijay P.; Sivakumar, Bellie; H. Kashani, Mahsa; Atre, Atul Arvind; Asadi, Hakimeh

2017-05-01

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

Ocular biometric parameters among 3-year-old Chinese children: testability, distribution and association with anthropometric parameters

PubMed Central

Huang, Dan; Chen, Xuejuan; Gong, Qi; Yuan, Chaoqun; Ding, Hui; Bai, Jing; Zhu, Hui; Fu, Zhujun; Yu, Rongbin; Liu, Hu

2016-01-01

This survey was conducted to determine the testability, distribution and associations of ocular biometric parameters in Chinese preschool children. Ocular biometric examinations, including the axial length (AL) and corneal radius of curvature (CR), were conducted on 1,688 3-year-old subjects by using an IOLMaster in August 2015. Anthropometric parameters, including height and weight, were measured according to a standardized protocol, and body mass index (BMI) was calculated. The testability was 93.7% for the AL and 78.6% for the CR overall, and both measures improved with age. Girls performed slightly better in AL measurements (P = 0.08), and the difference in CR was statistically significant (P < 0.05). The AL distribution was normal in girls (P = 0.12), whereas it was not in boys (P < 0.05). For CR1, all subgroups presented normal distributions (P = 0.16 for boys; P = 0.20 for girls), but the distribution varied when the subgroups were combined (P < 0.05). CR2 presented a normal distribution (P = 0.11), whereas the AL/CR ratio was abnormal (P < 0.001). Boys exhibited a significantly longer AL, a greater CR and a greater AL/CR ratio than girls (all P < 0.001). PMID:27384307

Predicting the required number of training samples. [for remotely sensed image data based on covariance matrix estimate quality criterion of normal distribution

NASA Technical Reports Server (NTRS)

Kalayeh, H. M.; Landgrebe, D. A.

1983-01-01

A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included. Previously announced in STAR as N82-28109

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.

Randomized path optimization for thevMitigated counter detection of UAVS

DTIC Science & Technology

2017-06-01

using Bayesian filtering . The KL divergence is used to compare the probability density of aircraft termination to a normal distribution around the...Bayesian filtering . The KL divergence is used to compare the probability density of aircraft termination to a normal distribution around the true terminal...algorithm’s success. A recursive Bayesian filtering scheme is used to assimilate noisy measurements of the UAVs position to predict its terminal location. We

Reply to: Are There More Gifted People than Would Be Expected on a Normal Distribution?

ERIC Educational Resources Information Center

Gallagher, James J.

2014-01-01

The author responds to the article by Warne, Godwin, and Smith (2013) on the question of whether there are more gifted people than would be expected in a Gaussian normal distribution. He asserts that the answer to this question is yes, based on (a) data that he and his colleagues have collected, (b) data that are already available and quoted by…

The force synergy of human digits in static and dynamic cylindrical grasps.

PubMed

Kuo, Li-Chieh; Chen, Shih-Wei; Lin, Chien-Ju; Lin, Wei-Jr; Lin, Sheng-Che; Su, Fong-Chin

2013-01-01

This study explores the force synergy of human digits in both static and dynamic cylindrical grasping conditions. The patterns of digit force distribution, error compensation, and the relationships among digit forces are examined to quantify the synergetic patterns and coordination of multi-finger movements. This study recruited 24 healthy participants to perform cylindrical grasps using a glass simulator under normal grasping and one-finger restricted conditions. Parameters such as the grasping force, patterns of digit force distribution, and the force coefficient of variation are determined. Correlation coefficients and principal component analysis (PCA) are used to estimate the synergy strength under the dynamic grasping condition. Specific distribution patterns of digit forces are identified for various conditions. The compensation of adjacent fingers for the force in the normal direction of an absent finger agrees with the principle of error compensation. For digit forces in anti-gravity directions, the distribution patterns vary significantly by participant. The forces exerted by the thumb are closely related to those exerted by other fingers under all conditions. The index-middle and middle-ring finger pairs demonstrate a significant relationship. The PCA results show that the normal forces of digits are highly coordinated. This study reveals that normal force synergy exists under both static and dynamic cylindrical grasping conditions.

The Force Synergy of Human Digits in Static and Dynamic Cylindrical Grasps

PubMed Central

Kuo, Li-Chieh; Chen, Shih-Wei; Lin, Chien-Ju; Lin, Wei-Jr; Lin, Sheng-Che; Su, Fong-Chin

2013-01-01

This study explores the force synergy of human digits in both static and dynamic cylindrical grasping conditions. The patterns of digit force distribution, error compensation, and the relationships among digit forces are examined to quantify the synergetic patterns and coordination of multi-finger movements. This study recruited 24 healthy participants to perform cylindrical grasps using a glass simulator under normal grasping and one-finger restricted conditions. Parameters such as the grasping force, patterns of digit force distribution, and the force coefficient of variation are determined. Correlation coefficients and principal component analysis (PCA) are used to estimate the synergy strength under the dynamic grasping condition. Specific distribution patterns of digit forces are identified for various conditions. The compensation of adjacent fingers for the force in the normal direction of an absent finger agrees with the principle of error compensation. For digit forces in anti-gravity directions, the distribution patterns vary significantly by participant. The forces exerted by the thumb are closely related to those exerted by other fingers under all conditions. The index-middle and middle-ring finger pairs demonstrate a significant relationship. The PCA results show that the normal forces of digits are highly coordinated. This study reveals that normal force synergy exists under both static and dynamic cylindrical grasping conditions. PMID:23544151

Parameter estimation for the exponential-normal convolution model for background correction of affymetrix GeneChip data.

PubMed

McGee, Monnie; Chen, Zhongxue

2006-01-01

There are many methods of correcting microarray data for non-biological sources of error. Authors routinely supply software or code so that interested analysts can implement their methods. Even with a thorough reading of associated references, it is not always clear how requisite parts of the method are calculated in the software packages. However, it is important to have an understanding of such details, as this understanding is necessary for proper use of the output, or for implementing extensions to the model. In this paper, the calculation of parameter estimates used in Robust Multichip Average (RMA), a popular preprocessing algorithm for Affymetrix GeneChip brand microarrays, is elucidated. The background correction method for RMA assumes that the perfect match (PM) intensities observed result from a convolution of the true signal, assumed to be exponentially distributed, and a background noise component, assumed to have a normal distribution. A conditional expectation is calculated to estimate signal. Estimates of the mean and variance of the normal distribution and the rate parameter of the exponential distribution are needed to calculate this expectation. Simulation studies show that the current estimates are flawed; therefore, new ones are suggested. We examine the performance of preprocessing under the exponential-normal convolution model using several different methods to estimate the parameters.

Distribution of runup heights of the December 26, 2004 tsunami in the Indian Ocean

NASA Astrophysics Data System (ADS)

Choi, Byung Ho; Hong, Sung Jin; Pelinovsky, Efim

2006-07-01

A massive earthquake with magnitude 9.3 occurred on December 26, 2004 off the northern Sumatra generated huge tsunami waves affected many coastal countries in the Indian Ocean. A number of field surveys have been performed after this tsunami event; in particular, several surveys in the south/east coast of India, Andaman and Nicobar Islands, Sri Lanka, Sumatra, Malaysia, and Thailand have been organized by the Korean Society of Coastal and Ocean Engineers from January to August 2005. Spatial distribution of the tsunami runup is used to analyze the distribution function of the wave heights on different coasts. Theoretical interpretation of this distribution is associated with random coastal bathymetry and coastline led to the log-normal functions. Observed data also are in a very good agreement with log-normal distribution confirming the important role of the variable ocean bathymetry in the formation of the irregular wave height distribution along the coasts.

An estimate of field size distributions for selected sites in the major grain producing countries

NASA Technical Reports Server (NTRS)

Podwysocki, M. H.

1977-01-01

The field size distributions for the major grain producing countries of the World were estimated. LANDSAT-1 and 2 images were evaluated for two areas each in the United States, People's Republic of China, and the USSR. One scene each was evaluated for France, Canada, and India. Grid sampling was done for representative sub-samples of each image, measuring the long and short axes of each field; area was then calculated. Each of the resulting data sets was computer analyzed for their frequency distributions. Nearly all frequency distributions were highly peaked and skewed (shifted) towards small values, approaching that of either a Poisson or log-normal distribution. The data were normalized by a log transformation, creating a Gaussian distribution which has moments readily interpretable and useful for estimating the total population of fields. Resultant predictors of the field size estimates are discussed.

The missing impact craters on Venus

NASA Technical Reports Server (NTRS)

Speidel, D. H.

1993-01-01

The size-frequency pattern of the 842 impact craters on Venus measured to date can be well described (across four standard deviation units) as a single log normal distribution with a mean crater diameter of 14.5 km. This result was predicted in 1991 on examination of the initial Magellan analysis. If this observed distribution is close to the real distribution, the 'missing' 90 percent of the small craters and the 'anomalous' lack of surface splotches may thus be neither missing nor anomalous. I think that the missing craters and missing splotches can be satisfactorily explained by accepting that the observed distribution approximates the real one, that it is not craters that are missing but the impactors. What you see is what you got. The implication that Venus crossing impactors would have the same type of log normal distribution is consistent with recently described distribution for terrestrial craters and Earth crossing asteroids.

On the issues of probability distribution of GPS carrier phase observations

NASA Astrophysics Data System (ADS)

Luo, X.; Mayer, M.; Heck, B.

2009-04-01

In common practice the observables related to Global Positioning System (GPS) are assumed to follow a Gauss-Laplace normal distribution. Actually, full knowledge of the observables' distribution is not required for parameter estimation by means of the least-squares algorithm based on the functional relation between observations and unknown parameters as well as the associated variance-covariance matrix. However, the probability distribution of GPS observations plays a key role in procedures for quality control (e.g. outlier and cycle slips detection, ambiguity resolution) and in reliability-related assessments of the estimation results. Under non-ideal observation conditions with respect to the factors impacting GPS data quality, for example multipath effects and atmospheric delays, the validity of the normal distribution postulate of GPS observations is in doubt. This paper presents a detailed analysis of the distribution properties of GPS carrier phase observations using double difference residuals. For this purpose 1-Hz observation data from the permanent SAPOS

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

Comparison of parametric and bootstrap method in bioequivalence test.

PubMed

Ahn, Byung-Jin; Yim, Dong-Seok

2009-10-01

The estimation of 90% parametric confidence intervals (CIs) of mean AUC and Cmax ratios in bioequivalence (BE) tests are based upon the assumption that formulation effects in log-transformed data are normally distributed. To compare the parametric CIs with those obtained from nonparametric methods we performed repeated estimation of bootstrap-resampled datasets. The AUC and Cmax values from 3 archived datasets were used. BE tests on 1,000 resampled datasets from each archived dataset were performed using SAS (Enterprise Guide Ver.3). Bootstrap nonparametric 90% CIs of formulation effects were then compared with the parametric 90% CIs of the original datasets. The 90% CIs of formulation effects estimated from the 3 archived datasets were slightly different from nonparametric 90% CIs obtained from BE tests on resampled datasets. Histograms and density curves of formulation effects obtained from resampled datasets were similar to those of normal distribution. However, in 2 of 3 resampled log (AUC) datasets, the estimates of formulation effects did not follow the Gaussian distribution. Bias-corrected and accelerated (BCa) CIs, one of the nonparametric CIs of formulation effects, shifted outside the parametric 90% CIs of the archived datasets in these 2 non-normally distributed resampled log (AUC) datasets. Currently, the 80~125% rule based upon the parametric 90% CIs is widely accepted under the assumption of normally distributed formulation effects in log-transformed data. However, nonparametric CIs may be a better choice when data do not follow this assumption.

Comparison of Parametric and Bootstrap Method in Bioequivalence Test

PubMed Central

Ahn, Byung-Jin

2009-01-01

The estimation of 90% parametric confidence intervals (CIs) of mean AUC and Cmax ratios in bioequivalence (BE) tests are based upon the assumption that formulation effects in log-transformed data are normally distributed. To compare the parametric CIs with those obtained from nonparametric methods we performed repeated estimation of bootstrap-resampled datasets. The AUC and Cmax values from 3 archived datasets were used. BE tests on 1,000 resampled datasets from each archived dataset were performed using SAS (Enterprise Guide Ver.3). Bootstrap nonparametric 90% CIs of formulation effects were then compared with the parametric 90% CIs of the original datasets. The 90% CIs of formulation effects estimated from the 3 archived datasets were slightly different from nonparametric 90% CIs obtained from BE tests on resampled datasets. Histograms and density curves of formulation effects obtained from resampled datasets were similar to those of normal distribution. However, in 2 of 3 resampled log (AUC) datasets, the estimates of formulation effects did not follow the Gaussian distribution. Bias-corrected and accelerated (BCa) CIs, one of the nonparametric CIs of formulation effects, shifted outside the parametric 90% CIs of the archived datasets in these 2 non-normally distributed resampled log (AUC) datasets. Currently, the 80~125% rule based upon the parametric 90% CIs is widely accepted under the assumption of normally distributed formulation effects in log-transformed data. However, nonparametric CIs may be a better choice when data do not follow this assumption. PMID:19915699

Optical and physical properties of stratospheric aerosols from balloon measurements in the visible and near-infrared domains. I. Analysis of aerosol extinction spectra from the AMON and SALOMON balloonborne spectrometers

NASA Astrophysics Data System (ADS)

Berthet, Gwenaël; Renard, Jean-Baptiste; Brogniez, Colette; Robert, Claude; Chartier, Michel; Pirre, Michel

2002-12-01

Aerosol extinction coefficients have been derived in the 375-700-nm spectral domain from measurements in the stratosphere since 1992, at night, at mid- and high latitudes from 15 to 40 km, by two balloonborne spectrometers, Absorption par les Minoritaires Ozone et NOx (AMON) and Spectroscopie d'Absorption Lunaire pour l'Observation des Minoritaires Ozone et NOx (SALOMON). Log-normal size distributions associated with the Mie-computed extinction spectra that best fit the measurements permit calculation of integrated properties of the distributions. Although measured extinction spectra that correspond to background aerosols can be reproduced by the Mie scattering model by use of monomodal log-normal size distributions, each flight reveals some large discrepancies between measurement and theory at several altitudes. The agreement between measured and Mie-calculated extinction spectra is significantly improved by use of bimodal log-normal distributions. Nevertheless, neither monomodal nor bimodal distributions permit correct reproduction of some of the measured extinction shapes, especially for the 26 February 1997 AMON flight, which exhibited spectral behavior attributed to particles from a polar stratospheric cloud event.

STUDIES ON THE DISTRIBUTION AND PHOSPHATE TURNOVER OF THE ACID-SOLUBLE PHOSPHORUS COMPOUNDS IN VARIOUS NORMAL AND NEOPLASTIC TISSUES OF RATS. II. COMPARISON OF THE CHROMATOGRAMS OBTAINED WITH VARIOUS TISSUES INCLUDING TUMOURS (ENGLISH TEXT)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horie, S.

Using a modified semi-micro gradient elution method of chromatography, the distribution of the acid-soluble nucleotides in various normal and neoplastic tissues of rats was compared and the variations of the distribution are described. The distribution and phosphate turnover of the acid-soluble phosphorus compounds were also studied by intraperitoneal injection of P/sup 32/ followed by the chromatographic analysis. The distribution patterns of nucleotides and radioactivity in liver, muscle, heart, lung, thymus, spleen, testicles, brain, fetal liver, and experimental hepatomas are illustrated and the differences between these tissues were pointed out. The characteristics of the experimental hepatoma tissue as compared with themore » normal liver tissue are as follows: The concentration of oxidized DPN was low; the incorporation of P/sup 32/ inorganic phosphate into glucose 6-phosphate and L- alpha -glycerophosphate was absent or, if any, very low; radioactivity of inorganic phosphate in the total acid-soluble radioactivity was extraordinarily high as compared with other tissues besides the liver tissue. (Abstr. Japan Med., 1: No. 9, 1961)« less

Ventilation-perfusion distribution in normal subjects.

PubMed

Beck, Kenneth C; Johnson, Bruce D; Olson, Thomas P; Wilson, Theodore A

2012-09-01

Functional values of LogSD of the ventilation distribution (σ(V)) have been reported previously, but functional values of LogSD of the perfusion distribution (σ(q)) and the coefficient of correlation between ventilation and perfusion (ρ) have not been measured in humans. Here, we report values for σ(V), σ(q), and ρ obtained from wash-in data for three gases, helium and two soluble gases, acetylene and dimethyl ether. Normal subjects inspired gas containing the test gases, and the concentrations of the gases at end-expiration during the first 10 breaths were measured with the subjects at rest and at increasing levels of exercise. The regional distribution of ventilation and perfusion was described by a bivariate log-normal distribution with parameters σ(V), σ(q), and ρ, and these parameters were evaluated by matching the values of expired gas concentrations calculated for this distribution to the measured values. Values of cardiac output and LogSD ventilation/perfusion (Va/Q) were obtained. At rest, σ(q) is high (1.08 ± 0.12). With the onset of ventilation, σ(q) decreases to 0.85 ± 0.09 but remains higher than σ(V) (0.43 ± 0.09) at all exercise levels. Rho increases to 0.87 ± 0.07, and the value of LogSD Va/Q for light and moderate exercise is primarily the result of the difference between the magnitudes of σ(q) and σ(V). With known values for the parameters, the bivariate distribution describes the comprehensive distribution of ventilation and perfusion that underlies the distribution of the Va/Q ratio.

Physiology and pathophysiology of potassium homeostasis.

PubMed

Palmer, Biff F; Clegg, Deborah J

2016-12-01

Total body potassium content and proper distribution of potassium across the cell membrane is of critical importance for normal cellular function. Potassium homeostasis is maintained by several different methods. In the kidney, total body potassium content is achieved by alterations in renal excretion of potassium in response to variations in intake. Insulin and beta-adrenergic tone play critical roles in maintaining the internal distribution of potassium under normal conditions. Despite homeostatic pathways designed to maintain potassium levels within the normal range, disorders of altered potassium homeostasis are common. The clinical approach to designing effective treatments relies on understanding the pathophysiology and regulatory influences which govern the internal distribution and external balance of potassium. Here we provide an overview of the key regulatory aspects of normal potassium physiology. This review is designed to provide an overview of potassium homeostasis as well as provide references of seminal papers to guide the reader into a more in depth discussion of the importance of potassium balance. This review is designed to be a resource for educators and well-informed clinicians who are teaching trainees about the importance of potassium balance. Copyright © 2016 the American Physiological Society.

Modeling absolute differences in life expectancy with a censored skew-normal regression approach

PubMed Central

Clough-Gorr, Kerri; Zwahlen, Marcel

2015-01-01

Parameter estimates from commonly used multivariable parametric survival regression models do not directly quantify differences in years of life expectancy. Gaussian linear regression models give results in terms of absolute mean differences, but are not appropriate in modeling life expectancy, because in many situations time to death has a negative skewed distribution. A regression approach using a skew-normal distribution would be an alternative to parametric survival models in the modeling of life expectancy, because parameter estimates can be interpreted in terms of survival time differences while allowing for skewness of the distribution. In this paper we show how to use the skew-normal regression so that censored and left-truncated observations are accounted for. With this we model differences in life expectancy using data from the Swiss National Cohort Study and from official life expectancy estimates and compare the results with those derived from commonly used survival regression models. We conclude that a censored skew-normal survival regression approach for left-truncated observations can be used to model differences in life expectancy across covariates of interest. PMID:26339544

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

NASA Astrophysics Data System (ADS)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

Using RxNorm for cross-institutional formulary data normalization within a distributed grid-computing environment.

PubMed

Wynden, Rob; Anderson, Nick; Casale, Marco; Lakshminarayanan, Prakash; Anderson, Kent; Prosser, Justin; Errecart, Larry; Livshits, Alice; Thimman, Tim; Weiner, Mark

2011-01-01

Within the CTSA (Clinical Translational Sciences Awards) program, academic medical centers are tasked with the storage of clinical formulary data within an Integrated Data Repository (IDR) and the subsequent exposure of that data over grid computing environments for hypothesis generation and cohort selection. Formulary data collected over long periods of time across multiple institutions requires normalization of terms before those data sets can be aggregated and compared. This paper sets forth a solution to the challenge of generating derived aggregated normalized views from large, distributed data sets of clinical formulary data intended for re-use within clinical translational research.

The calculated influence of atmospheric conditions on solar cell ISC under direct and global solar irradiances

NASA Technical Reports Server (NTRS)

Mueller, Robert L.

1987-01-01

Calculations of the influence of atmospheric conditions on solar cell short-circuit current (Isc) are made using a recently developed computer model for solar spectral irradiance distribution. The results isolate the dependence of Isc on changes in the spectral irradiance distribution without the direct influence of the total irradiance level. The calculated direct normal irradiance and percent diffuse irradiance are given as a reference to indicate the expected irradiance levels. This method can be applied to the calibration of photovoltaic reference cells. Graphic examples are provided for amorphous silicon and monocrystalline silicon solar cells under direct normal and global normal solar irradiances.

Multivariate Models for Normal and Binary Responses in Intervention Studies

ERIC Educational Resources Information Center

Pituch, Keenan A.; Whittaker, Tiffany A.; Chang, Wanchen

2016-01-01

Use of multivariate analysis (e.g., multivariate analysis of variance) is common when normally distributed outcomes are collected in intervention research. However, when mixed responses--a set of normal and binary outcomes--are collected, standard multivariate analyses are no longer suitable. While mixed responses are often obtained in…

A Skew-Normal Mixture Regression Model

ERIC Educational Resources Information Center

Liu, Min; Lin, Tsung-I

2014-01-01

A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly…

A Robust Bayesian Approach for Structural Equation Models with Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Xia, Ye-Mao

2008-01-01

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…

On measures of association among genetic variables

PubMed Central

Gianola, Daniel; Manfredi, Eduardo; Simianer, Henner

2012-01-01

Summary Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution. Our measures are based on logarithmic (Kullback-Leibler) and on relative ‘distances’ between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart. PMID:22742500

An Empirical Study of Synchrophasor Communication Delay in a Utility TCP/IP Network

NASA Astrophysics Data System (ADS)

Zhu, Kun; Chenine, Moustafa; Nordström, Lars; Holmström, Sture; Ericsson, Göran

2013-07-01

Although there is a plethora of literature dealing with Phasor Measurement Unit (PMU) communication delay, there has not been any effort made to generalize empirical delay results by identifying the distribution with the best fit. The existing studies typically assume a distribution or simply build on analogies to communication network routing delay. Specifically, this study provides insight into the characterization of the communication delay of both unprocessed PMU data and synchrophasors sorted by a Phasor Data Concentrator (PDC). The results suggest that a bi-modal distribution containing two normal distributions offers the best fit of the delay of the unprocessed data, whereas the delay profile of the sorted synchrophasors resembles a normal distribution based on these results, the possibility of evaluating the reliability of a synchrophasor application with respect to a particular choice of PDC timeout is discussed.

Using the range to calculate the coefficient of variation.

PubMed

Rhiel, G Steven

2004-12-01

In this research a coefficient of variation (CVhigh-low) is calculated from the highest and lowest values in a set of data. Use of CVhigh-low when the population is normal, leptokurtic, and skewed is discussed. The statistic is the most effective when sampling from the normal distribution. With the leptokurtic distributions, CVhigh-low works well for comparing the relative variability between two or more distributions but does not provide a very "good" point estimate of the population coefficient of variation. With skewed distributions CVhigh-low works well in identifying which data set has the more relative variation but does not specify how much difference there is in the variation. It also does not provide a "good" point estimate.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soreq, Yotam; Zhu, Hua Xing; Zupan, Jure

We show that the normalized Higgs production p T and y h distributions are sensitive probes of Higgs couplings to light quarks. For up and/or down quark Yukawa couplings comparable to the SM b quark Yukawa themore » $$\\bar{u}u$$ or $$\\bar{d}d$$ fusion production of the Higgs could lead to appreciable softer p T distribution than in the SM. The rapidity distribution, on the other hand, becomes more forward. Here, we find that, owing partially to a downward fluctuation, one can derive competitive bounds on the two couplings using ATLAS measurements of normalized p T distribution at 8TeV. With 300 fb -1 at 13TeV LHC one could establish flavor non-universality of the Yukawa couplings in the down sector.« less

Pharmacokinetics and tissue distribution of five active ingredients of Eucommiae cortex in normal and ovariectomized mice by UHPLC-MS/MS.

PubMed

An, Jing; Hu, Fangdi; Wang, Changhong; Zhang, Zijia; Yang, Li; Wang, Zhengtao

2016-09-01

1. Pinoresinol di-O-β-d-glucopyranoside (PDG), geniposide (GE), geniposidic acid (GA), aucubin (AN) and chlorogenic acid (CA) are the representative active ingredients in Eucommiae cortex (EC), which may be estrogenic. 2. The ultra high-performance liquid chromatography/tandem mass spectrometry (UHPLC-MS/MS) method for simultaneous determination of the five ingredients showed good linearity, low limits of quantification and high extraction recoveries, as well as acceptable precision, accuracy and stability in mice plasma and tissue samples (liver, spleen, kidney and uterus). It was successfully applied to the comparative study on pharmacokinetics and tissue distribution of PDG, GE, GA, AN and CA between normal and ovariectomized (OVX) mice. 3. The results indicated that except CA, the plasma and tissue concentrations of PDG, GE, GA in OVX mice were all greater than those in normal mice. AN could only be detected in the plasma and liver homogenate of normal mice, which was poorly absorbed in OVX mice and low in other measured tissues. PDG, GE and GA seem to be better absorbed in OVX mice than in normal mice proved by the remarkable increased value of AUC0-∞ and Cmax. It is beneficial that PDG, GE, GA have better plasma absorption and tissue distribution in pathological state.

Determining prescription durations based on the parametric waiting time distribution.

PubMed

Støvring, Henrik; Pottegård, Anton; Hallas, Jesper

2016-12-01

The purpose of the study is to develop a method to estimate the duration of single prescriptions in pharmacoepidemiological studies when the single prescription duration is not available. We developed an estimation algorithm based on maximum likelihood estimation of a parametric two-component mixture model for the waiting time distribution (WTD). The distribution component for prevalent users estimates the forward recurrence density (FRD), which is related to the distribution of time between subsequent prescription redemptions, the inter-arrival density (IAD), for users in continued treatment. We exploited this to estimate percentiles of the IAD by inversion of the estimated FRD and defined the duration of a prescription as the time within which 80% of current users will have presented themselves again. Statistical properties were examined in simulation studies, and the method was applied to empirical data for four model drugs: non-steroidal anti-inflammatory drugs (NSAIDs), warfarin, bendroflumethiazide, and levothyroxine. Simulation studies found negligible bias when the data-generating model for the IAD coincided with the FRD used in the WTD estimation (Log-Normal). When the IAD consisted of a mixture of two Log-Normal distributions, but was analyzed with a single Log-Normal distribution, relative bias did not exceed 9%. Using a Log-Normal FRD, we estimated prescription durations of 117, 91, 137, and 118 days for NSAIDs, warfarin, bendroflumethiazide, and levothyroxine, respectively. Similar results were found with a Weibull FRD. The algorithm allows valid estimation of single prescription durations, especially when the WTD reliably separates current users from incident users, and may replace ad-hoc decision rules in automated implementations. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Technical note: An improved approach to determining background aerosol concentrations with PILS sampling on aircraft

NASA Astrophysics Data System (ADS)

Fukami, Christine S.; Sullivan, Amy P.; Ryan Fulgham, S.; Murschell, Trey; Borch, Thomas; Smith, James N.; Farmer, Delphine K.

2016-07-01

Particle-into-Liquid Samplers (PILS) have become a standard aerosol collection technique, and are widely used in both ground and aircraft measurements in conjunction with off-line ion chromatography (IC) measurements. Accurate and precise background samples are essential to account for gas-phase components not efficiently removed and any interference in the instrument lines, collection vials or off-line analysis procedures. For aircraft sampling with PILS, backgrounds are typically taken with in-line filters to remove particles prior to sample collection once or twice per flight with more numerous backgrounds taken on the ground. Here, we use data collected during the Front Range Air Pollution and Photochemistry Éxperiment (FRAPPÉ) to demonstrate that not only are multiple background filter samples are essential to attain a representative background, but that the chemical background signals do not follow the Gaussian statistics typically assumed. Instead, the background signals for all chemical components analyzed from 137 background samples (taken from ∼78 total sampling hours over 18 flights) follow a log-normal distribution, meaning that the typical approaches of averaging background samples and/or assuming a Gaussian distribution cause an over-estimation of background samples - and thus an underestimation of sample concentrations. Our approach of deriving backgrounds from the peak of the log-normal distribution results in detection limits of 0.25, 0.32, 3.9, 0.17, 0.75 and 0.57 μg m-3 for sub-micron aerosol nitrate (NO3-), nitrite (NO2-), ammonium (NH4+), sulfate (SO42-), potassium (K+) and calcium (Ca2+), respectively. The difference in backgrounds calculated from assuming a Gaussian distribution versus a log-normal distribution were most extreme for NH4+, resulting in a background that was 1.58× that determined from fitting a log-normal distribution.

Influence of Transformation Plasticity on the Distribution of Internal Stress in Three Water-Quenched Cylinders

NASA Astrophysics Data System (ADS)

Liu, Yu; Qin, Shengwei; Zhang, Jiazhi; Wang, Ying; Rong, Yonghua; Zuo, Xunwei; Chen, Nailu

2017-10-01

Based on the hardenability of three medium carbon steels, cylinders with the same 60-mm diameter and 240-mm length were designed for quenching in water to obtain microstructures, including a pearlite matrix (Chinese steel mark: 45), a bainite matrix (42CrMo), and a martensite matrix (40CrNiMo). Through the combination of normalized functions describing transformation plasticity (TP), the thermo-elasto-plastic constitutive equation was deduced. The results indicate that the finite element simulation (FES) of the internal stress distribution in the three kinds of hardenable steel cylinders based on the proposed exponent-modified (Ex-Modified) normalized function is more consistent with the X-ray diffraction (XRD) measurements than those based on the normalized functions proposed by Abrassart, Desalos, and Leblond, which is attributed to the fact that the Ex-Modified normalized function better describes the TP kinetics. In addition, there was no significant difference between the calculated and measured stress distributions, even though TP was taken into account for the 45 carbon steel; that is, TP can be ignored in FES. In contrast, in the 42CrMo and 40CrNiMo alloyed steels, the significant effect of TP on the residual stress distributions was demonstrated, meaning that TP must be included in the FES. The rationality of the preceding conclusions was analyzed. The complex quenching stress is a consequence of interactions between the thermal and phase transformation stresses. The separated calculations indicate that the three steels exhibit similar thermal stress distributions for the same water-quenching condition, but different phase transformation stresses between 45 carbon steel and alloyed steels, leading to different distributions of their axial and tangential stresses.

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

PubMed Central

Neti, Prasad V.S.V.; Howell, Roger W.

2010-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log-normal (LN) distribution function (J Nucl Med. 2006;47:1049–1058) with the aid of autoradiography. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analysis of these earlier data. Methods The measured distributions of α-particle tracks per cell were subjected to statistical tests with Poisson, LN, and Poisson-lognormal (P-LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL of 210Po-citrate. When cells were exposed to 67 kBq/mL, the P-LN distribution function gave a better fit; however, the underlying activity distribution remained log-normal. Conclusion The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:18483086

Spatial analysis of cities using Renyi entropy and fractal parameters

NASA Astrophysics Data System (ADS)

Chen, Yanguang; Feng, Jian

2017-12-01

The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is not suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to generalizing multifractal parameters by means of dual relation between Euclidean and fractal geometries. The main method is mathematical derivation and empirical analysis, and the theoretical foundation is the discovery that the normalized fractal dimension is equal to the normalized entropy. Based on this finding, a set of useful spatial indexes termed dummy multifractal parameters are defined for geographical analysis. These indexes can be employed to describe both the simple distributions and complex distributions. The dummy multifractal indexes are applied to the population density distribution of Hangzhou city, China. The calculation results reveal the feature of spatio-temporal evolution of Hangzhou's urban morphology. This study indicates that fractal dimension and spatial entropy can be combined to produce a new methodology for spatial analysis of city development.

A normalization method for combination of laboratory test results from different electronic healthcare databases in a distributed research network.

PubMed

Yoon, Dukyong; Schuemie, Martijn J; Kim, Ju Han; Kim, Dong Ki; Park, Man Young; Ahn, Eun Kyoung; Jung, Eun-Young; Park, Dong Kyun; Cho, Soo Yeon; Shin, Dahye; Hwang, Yeonsoo; Park, Rae Woong

2016-03-01

Distributed research networks (DRNs) afford statistical power by integrating observational data from multiple partners for retrospective studies. However, laboratory test results across care sites are derived using different assays from varying patient populations, making it difficult to simply combine data for analysis. Additionally, existing normalization methods are not suitable for retrospective studies. We normalized laboratory results from different data sources by adjusting for heterogeneous clinico-epidemiologic characteristics of the data and called this the subgroup-adjusted normalization (SAN) method. Subgroup-adjusted normalization renders the means and standard deviations of distributions identical under population structure-adjusted conditions. To evaluate its performance, we compared SAN with existing methods for simulated and real datasets consisting of blood urea nitrogen, serum creatinine, hematocrit, hemoglobin, serum potassium, and total bilirubin. Various clinico-epidemiologic characteristics can be applied together in SAN. For simplicity of comparison, age and gender were used to adjust population heterogeneity in this study. In simulations, SAN had the lowest standardized difference in means (SDM) and Kolmogorov-Smirnov values for all tests (p < 0.05). In a real dataset, SAN had the lowest SDM and Kolmogorov-Smirnov values for blood urea nitrogen, hematocrit, hemoglobin, and serum potassium, and the lowest SDM for serum creatinine (p < 0.05). Subgroup-adjusted normalization performed better than normalization using other methods. The SAN method is applicable in a DRN environment and should facilitate analysis of data integrated across DRN partners for retrospective observational studies. Copyright © 2015 John Wiley & Sons, Ltd.

EVALUATION OF A NEW MEAN SCALED AND MOMENT ADJUSTED TEST STATISTIC FOR SEM.

PubMed

Tong, Xiaoxiao; Bentler, Peter M

2013-01-01

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and two well-known robust test statistics. A modification to the Satorra-Bentler scaled statistic is developed for the condition that sample size is smaller than degrees of freedom. The behavior of the four test statistics is evaluated with a Monte Carlo confirmatory factor analysis study that varies seven sample sizes and three distributional conditions obtained using Headrick's fifth-order transformation to nonnormality. The new statistic performs badly in most conditions except under the normal distribution. The goodness-of-fit χ(2) test based on maximum-likelihood estimation performed well under normal distributions as well as under a condition of asymptotic robustness. The Satorra-Bentler scaled test statistic performed best overall, while the mean scaled and variance adjusted test statistic outperformed the others at small and moderate sample sizes under certain distributional conditions.

Correlates of sexual risk behaviors among young Black MSM: implications for clinic-based counseling programs

PubMed Central

Crosby, Richard A.; Mena, Leandro; Ricks, JaNelle

2018-01-01

This study applied an 8-item index of recent sexual risk behaviors to young Black men who have sex with men (YBMSM) and evaluated the distribution for normality. The distribution was tested for associations with possible antecedents of sexual risk. YBMSM (N=600), ages 16–29 years, were recruited from an STI clinic, located in the Southern United States. Men completed an extensive audio-computer assisted self-interview. Thirteen possible antecedents of sexual risk, as assessed by the index, were selected for analyses. The 8-item index formed a normal distribution with a mean of 4.77 (sd=1.77). In adjusted analyses, not having completed education beyond high school was associated with less risk, as was having sex with females. Conversely, meeting sex partners online was associated with greater risk, as was reporting that sex partners were drunk during sex. The obtained normal distribution of sexual risk behaviors suggests a corresponding need to “target and tailor” clinic-based counseling and prevention services for YBMSM. Avoiding sex when partners are intoxicated may be an especially valuable goal of counseling sessions. PMID:27875903

Correlates of sexual-risk behaviors among young black MSM: implications for clinic-based counseling programs.

PubMed

Crosby, Richard A; Mena, Leandro; Ricks, JaNelle M

2017-06-01

This study applied an 8-item index of recent sexual-risk behaviors to young Black men who have sex with men (YBMSM) and evaluated the distribution for normality. The distribution was tested for associations with possible antecedents of sexual risk. YBMSM (N = 600), aged 16-29 years, were recruited from a sexually transmitted infection clinic, located in the southern US. Men completed an extensive audio computer-assisted self-interview. Thirteen possible antecedents of sexual risk, as assessed by the index, were selected for analyses. The 8-item index formed a normal distribution with a mean of 4.77 (SD = 1.77). In adjusted analyses, not having completed education beyond high school was associated with less risk, as was having sex with females. Conversely, meeting sex partners online was associated with greater risk, as was reporting that sex partners were drunk during sex. The obtained normal distribution of sexual-risk behaviors suggests a corresponding need to "target and tailor" clinic-based counseling and prevention services for YBMSM. Avoiding sex when partners are intoxicated may be an especially valuable goal of counseling sessions.

Comparison of Grand Median and Cumulative Sum Control Charts on Shuttlecock Weight Variable in CV Marjoko Kompas dan Domas

NASA Astrophysics Data System (ADS)

Musdalifah, N.; Handajani, S. S.; Zukhronah, E.

2017-06-01

Competition between the homoneous companies cause the company have to keep production quality. To cover this problem, the company controls the production with statistical quality control using control chart. Shewhart control chart is used to normal distributed data. The production data is often non-normal distribution and occured small process shift. Grand median control chart is a control chart for non-normal distributed data, while cumulative sum (cusum) control chart is a sensitive control chart to detect small process shift. The purpose of this research is to compare grand median and cusum control charts on shuttlecock weight variable in CV Marjoko Kompas dan Domas by generating data as the actual distribution. The generated data is used to simulate multiplier of standard deviation on grand median and cusum control charts. Simulation is done to get average run lenght (ARL) 370. Grand median control chart detects ten points that out of control, while cusum control chart detects a point out of control. It can be concluded that grand median control chart is better than cusum control chart.

Fundamentals of Research Data and Variables: The Devil Is in the Details.

PubMed

Vetter, Thomas R

2017-10-01

Designing, conducting, analyzing, reporting, and interpreting the findings of a research study require an understanding of the types and characteristics of data and variables. Descriptive statistics are typically used simply to calculate, describe, and summarize the collected research data in a logical, meaningful, and efficient way. Inferential statistics allow researchers to make a valid estimate of the association between an intervention and the treatment effect in a specific population, based upon their randomly collected, representative sample data. Categorical data can be either dichotomous or polytomous. Dichotomous data have only 2 categories, and thus are considered binary. Polytomous data have more than 2 categories. Unlike dichotomous and polytomous data, ordinal data are rank ordered, typically based on a numerical scale that is comprised of a small set of discrete classes or integers. Continuous data are measured on a continuum and can have any numeric value over this continuous range. Continuous data can be meaningfully divided into smaller and smaller or finer and finer increments, depending upon the precision of the measurement instrument. Interval data are a form of continuous data in which equal intervals represent equal differences in the property being measured. Ratio data are another form of continuous data, which have the same properties as interval data, plus a true definition of an absolute zero point, and the ratios of the values on the measurement scale make sense. The normal (Gaussian) distribution ("bell-shaped curve") is of the most common statistical distributions. Many applied inferential statistical tests are predicated on the assumption that the analyzed data follow a normal distribution. The histogram and the Q-Q plot are 2 graphical methods to assess if a set of data have a normal distribution (display "normality"). The Shapiro-Wilk test and the Kolmogorov-Smirnov test are 2 well-known and historically widely applied quantitative methods to assess for data normality. Parametric statistical tests make certain assumptions about the characteristics and/or parameters of the underlying population distribution upon which the test is based, whereas nonparametric tests make fewer or less rigorous assumptions. If the normality test concludes that the study data deviate significantly from a Gaussian distribution, rather than applying a less robust nonparametric test, the problem can potentially be remedied by judiciously and openly: (1) performing a data transformation of all the data values; or (2) eliminating any obvious data outlier(s).

Log-Normal Turbulence Dissipation in Global Ocean Models

NASA Astrophysics Data System (ADS)

Pearson, Brodie; Fox-Kemper, Baylor

2018-03-01

Data from turbulent numerical simulations of the global ocean demonstrate that the dissipation of kinetic energy obeys a nearly log-normal distribution even at large horizontal scales O (10 km ) . As the horizontal scales of resolved turbulence are larger than the ocean is deep, the Kolmogorov-Yaglom theory for intermittency in 3D homogeneous, isotropic turbulence cannot apply; instead, the down-scale potential enstrophy cascade of quasigeostrophic turbulence should. Yet, energy dissipation obeys approximate log-normality—robustly across depths, seasons, regions, and subgrid schemes. The distribution parameters, skewness and kurtosis, show small systematic departures from log-normality with depth and subgrid friction schemes. Log-normality suggests that a few high-dissipation locations dominate the integrated energy and enstrophy budgets, which should be taken into account when making inferences from simplified models and inferring global energy budgets from sparse observations.

Rough Sets and Stomped Normal Distribution for Simultaneous Segmentation and Bias Field Correction in Brain MR Images.

PubMed

Banerjee, Abhirup; Maji, Pradipta

2015-12-01

The segmentation of brain MR images into different tissue classes is an important task for automatic image analysis technique, particularly due to the presence of intensity inhomogeneity artifact in MR images. In this regard, this paper presents a novel approach for simultaneous segmentation and bias field correction in brain MR images. It integrates judiciously the concept of rough sets and the merit of a novel probability distribution, called stomped normal (SN) distribution. The intensity distribution of a tissue class is represented by SN distribution, where each tissue class consists of a crisp lower approximation and a probabilistic boundary region. The intensity distribution of brain MR image is modeled as a mixture of finite number of SN distributions and one uniform distribution. The proposed method incorporates both the expectation-maximization and hidden Markov random field frameworks to provide an accurate and robust segmentation. The performance of the proposed approach, along with a comparison with related methods, is demonstrated on a set of synthetic and real brain MR images for different bias fields and noise levels.

Height and the normal distribution: evidence from Italian military data.

PubMed

A'Hearn, Brian; Peracchi, Franco; Vecchi, Giovanni

2009-02-01

Researchers modeling historical heights have typically relied on the restrictive assumption of a normal distribution, only the mean of which is affected by age, income, nutrition, disease, and similar influences. To avoid these restrictive assumptions, we develop a new semiparametric approach in which covariates are allowed to affect the entire distribution without imposing any parametric shape. We apply our method to a new database of height distributions for Italian provinces, drawn from conscription records, of unprecedented length and geographical disaggregation. Our method allows us to standardize distributions to a single age and calculate moments of the distribution that are comparable through time. Our method also allows us to generate counterfactual distributions for a range of ages, from which we derive age-height profiles. These profiles reveal how the adolescent growth spurt (AGS) distorts the distribution of stature, and they document the earlier and earlier onset of the AGS as living conditions improved over the second half of the nineteenth century. Our new estimates of provincial mean height also reveal a previously unnoticed "regime switch "from regional convergence to divergence in this period.

A comparative study of a theoretical neural net model with MEG data from epileptic patients and normal individuals.

PubMed

Kotini, A; Anninos, P; Anastasiadis, A N; Tamiolakis, D

2005-09-07

The aim of this study was to compare a theoretical neural net model with MEG data from epileptic patients and normal individuals. Our experimental study population included 10 epilepsy sufferers and 10 healthy subjects. The recordings were obtained with a one-channel biomagnetometer SQUID in a magnetically shielded room. Using the method of x2-fitting it was found that the MEG amplitudes in epileptic patients and normal subjects had Poisson and Gauss distributions respectively. The Poisson connectivity derived from the theoretical neural model represents the state of epilepsy, whereas the Gauss connectivity represents normal behavior. The MEG data obtained from epileptic areas had higher amplitudes than the MEG from normal regions and were comparable with the theoretical magnetic fields from Poisson and Gauss distributions. Furthermore, the magnetic field derived from the theoretical model had amplitudes in the same order as the recorded MEG from the 20 participants. The approximation of the theoretical neural net model with real MEG data provides information about the structure of the brain function in epileptic and normal states encouraging further studies to be conducted.

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1983-01-01

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.

Probabilistic structural analysis of a truss typical for space station

NASA Technical Reports Server (NTRS)

Pai, Shantaram S.

1990-01-01

A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.

A New Distribution Family for Microarray Data †

PubMed Central

Kelmansky, Diana Mabel; Ricci, Lila

2017-01-01

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative standpoint taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. R codes are available from the authors upon request. PMID:28208652

A New Distribution Family for Microarray Data.

PubMed

Kelmansky, Diana Mabel; Ricci, Lila

2017-02-10

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative stand point taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. Rcodes are available from the authors upon request.

Are your covariates under control? How normalization can re-introduce covariate effects.

PubMed

Pain, Oliver; Dudbridge, Frank; Ronald, Angelica

2018-04-30

Many statistical tests rely on the assumption that the residuals of a model are normally distributed. Rank-based inverse normal transformation (INT) of the dependent variable is one of the most popular approaches to satisfy the normality assumption. When covariates are included in the analysis, a common approach is to first adjust for the covariates and then normalize the residuals. This study investigated the effect of regressing covariates against the dependent variable and then applying rank-based INT to the residuals. The correlation between the dependent variable and covariates at each stage of processing was assessed. An alternative approach was tested in which rank-based INT was applied to the dependent variable before regressing covariates. Analyses based on both simulated and real data examples demonstrated that applying rank-based INT to the dependent variable residuals after regressing out covariates re-introduces a linear correlation between the dependent variable and covariates, increasing type-I errors and reducing power. On the other hand, when rank-based INT was applied prior to controlling for covariate effects, residuals were normally distributed and linearly uncorrelated with covariates. This latter approach is therefore recommended in situations were normality of the dependent variable is required.

DISFIT: A PROGRAM FOR FITTING DISTRIBUTIONS IN DATA

EPA Science Inventory

Although distribution fitting methods abound in the statistical literature, very few of these methods are found in the major statistical packages. In particular, SPSS (1975), BMD-P (1981) and SAS (1979) only give some overall tests for normality. There a few specialized distribut...

Realized Volatility Analysis in A Spin Model of Financial Markets

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

We calculate the realized volatility of returns in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard normal variables. This is the first evidence that the return distributions of the spin financial markets are consistent with a finite-variance of mixture of normal distributions that is also observed empirically in real financial markets.

The behaviour of cross-helicity and residual energy at different heliolatitudes - Ulysses data

NASA Astrophysics Data System (ADS)

Popescu, Emil; Popescu, Nedelia Antonia

In this paper we analyze the variations of the normalized cross-helicity (?C ) and normalized residual energy (σR), that characterize the Alfvenic fluctuations in the solar wind. For this purpose we consider data from SWOOPS and VHM instruments on board of Ulysses mission, for solar wind plasma parameters and magnetic field data, for the year 2001. In order to analyze the behaviour of the normalized cross-helicity, σC, and normalized residual energy, σR, at different heliolatitudes, as well as the relation between σR and σC, we determine their distributions for three periods of time: DOY 240 - DOY 348 (for a data sample at high heliolatitudes, between 69°N - 82.2°N), DOY 154 - DOY 181.5 (for a data sample at middle heliolatitudes, between 15°N - 35°N), and DOY 88 - DOY 118 (for a data sample at middle heliolatitudes, between 15°S - 35°S). The results on the residual energy σR versus cross-helicity σC distribution reveal a middle heliolatitude data sample that presents a more dispersed distribution than the high heliolatitude data sample. A different behaviour of the σC distributions was observed for the periods covering the middle heliolatitudes for the southern and northern hemispheres. This is because during the third period of time, transient events as ICMEs with strong magnetic field strength and high velocity are encountered.

Identifying Epigenetic Biomarkers using Maximal Relevance and Minimal Redundancy Based Feature Selection for Multi-Omics Data.

PubMed

Mallik, Saurav; Bhadra, Tapas; Maulik, Ujjwal

2017-01-01

Epigenetic Biomarker discovery is an important task in bioinformatics. In this article, we develop a new framework of identifying statistically significant epigenetic biomarkers using maximal-relevance and minimal-redundancy criterion based feature (gene) selection for multi-omics dataset. Firstly, we determine the genes that have both expression as well as methylation values, and follow normal distribution. Similarly, we identify the genes which consist of both expression and methylation values, but do not follow normal distribution. For each case, we utilize a gene-selection method that provides maximal-relevant, but variable-weighted minimum-redundant genes as top ranked genes. For statistical validation, we apply t-test on both the expression and methylation data consisting of only the normally distributed top ranked genes to determine how many of them are both differentially expressed andmethylated. Similarly, we utilize Limma package for performing non-parametric Empirical Bayes test on both expression and methylation data comprising only the non-normally distributed top ranked genes to identify how many of them are both differentially expressed and methylated. We finally report the top-ranking significant gene-markerswith biological validation. Moreover, our framework improves positive predictive rate and reduces false positive rate in marker identification. In addition, we provide a comparative analysis of our gene-selection method as well as othermethods based on classificationperformances obtained using several well-known classifiers.

Statistical distributions of ultra-low dose CT sinograms and their fundamental limits

NASA Astrophysics Data System (ADS)

Lee, Tzu-Cheng; Zhang, Ruoqiao; Alessio, Adam M.; Fu, Lin; De Man, Bruno; Kinahan, Paul E.

2017-03-01

Low dose CT imaging is typically constrained to be diagnostic. However, there are applications for even lowerdose CT imaging, including image registration across multi-frame CT images and attenuation correction for PET/CT imaging. We define this as the ultra-low-dose (ULD) CT regime where the exposure level is a factor of 10 lower than current low-dose CT technique levels. In the ULD regime it is possible to use statistically-principled image reconstruction methods that make full use of the raw data information. Since most statistical based iterative reconstruction methods are based on the assumption of that post-log noise distribution is close to Poisson or Gaussian, our goal is to understand the statistical distribution of ULD CT data with different non-positivity correction methods, and to understand when iterative reconstruction methods may be effective in producing images that are useful for image registration or attenuation correction in PET/CT imaging. We first used phantom measurement and calibrated simulation to reveal how the noise distribution deviate from normal assumption under the ULD CT flux environment. In summary, our results indicate that there are three general regimes: (1) Diagnostic CT, where post-log data are well modeled by normal distribution. (2) Lowdose CT, where normal distribution remains a reasonable approximation and statistically-principled (post-log) methods that assume a normal distribution have an advantage. (3) An ULD regime that is photon-starved and the quadratic approximation is no longer effective. For instance, a total integral density of 4.8 (ideal pi for 24 cm of water) for 120kVp, 0.5mAs of radiation source is the maximum pi value where a definitive maximum likelihood value could be found. This leads to fundamental limits in the estimation of ULD CT data when using a standard data processing stream

Breast cancer subtype distribution is different in normal weight, overweight, and obese women.

PubMed

Gershuni, Victoria; Li, Yun R; Williams, Austin D; So, Alycia; Steel, Laura; Carrigan, Elena; Tchou, Julia

2017-06-01

Obesity is associated with tumor promoting pathways related to insulin resistance and chronic low-grade inflammation which have been linked to various disease states, including cancer. Many studies have focused on the relationship between obesity and increased estrogen production, which contributes to the pathogenesis of estrogen receptor-positive breast cancers. The link between obesity and other breast cancer subtypes, such as triple-negative breast cancer (TNBC) and Her2/neu+ (Her2+) breast cancer, is less clear. We hypothesize that obesity may be associated with the pathogenesis of specific breast cancer subtypes resulting in a different subtype distribution than normal weight women. A single-institution, retrospective analysis of tumor characteristics of 848 patients diagnosed with primary operable breast cancer between 2000 and 2013 was performed to evaluate the association between BMI and clinical outcome. Patients were grouped based on their BMI at time of diagnosis stratified into three subgroups: normal weight (BMI = 18-24.9), overweight (BMI = 25-29.9), and obese (BMI > 30). The distribution of breast cancer subtypes across the three BMI subgroups was compared. Obese and overweight women were more likely to present with TNBC and normal weight women with Her2+ breast cancer (p = 0.008). We demonstrated, for the first time, that breast cancer subtype distribution varied significantly according to BMI status. Our results suggested that obesity might activate molecular pathways other than the well-known obesity/estrogen circuit in the pathogenesis of breast cancer. Future studies are needed to understand the molecular mechanisms that drive the variation in subtype distribution across BMI subgroups.

Comparison of Sample Size by Bootstrap and by Formulas Based on Normal Distribution Assumption.

PubMed

Wang, Zuozhen

2018-01-01

Bootstrapping technique is distribution-independent, which provides an indirect way to estimate the sample size for a clinical trial based on a relatively smaller sample. In this paper, sample size estimation to compare two parallel-design arms for continuous data by bootstrap procedure are presented for various test types (inequality, non-inferiority, superiority, and equivalence), respectively. Meanwhile, sample size calculation by mathematical formulas (normal distribution assumption) for the identical data are also carried out. Consequently, power difference between the two calculation methods is acceptably small for all the test types. It shows that the bootstrap procedure is a credible technique for sample size estimation. After that, we compared the powers determined using the two methods based on data that violate the normal distribution assumption. To accommodate the feature of the data, the nonparametric statistical method of Wilcoxon test was applied to compare the two groups in the data during the process of bootstrap power estimation. As a result, the power estimated by normal distribution-based formula is far larger than that by bootstrap for each specific sample size per group. Hence, for this type of data, it is preferable that the bootstrap method be applied for sample size calculation at the beginning, and that the same statistical method as used in the subsequent statistical analysis is employed for each bootstrap sample during the course of bootstrap sample size estimation, provided there is historical true data available that can be well representative of the population to which the proposed trial is planning to extrapolate.

Statistical characteristics of the spatial distribution of territorial contamination by radionuclides from the Chernobyl accident

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arutyunyan, R.V.; Bol`shov, L.A.; Vasil`ev, S.K.

1994-06-01

The objective of this study was to clarify a number of issues related to the spatial distribution of contaminants from the Chernobyl accident. The effects of local statistics were addressed by collecting and analyzing (for Cesium 137) soil samples from a number of regions, and it was found that sample activity differed by a factor of 3-5. The effect of local non-uniformity was estimated by modeling the distribution of the average activity of a set of five samples for each of the regions, with the spread in the activities for a {+-}2 range being equal to 25%. The statistical characteristicsmore » of the distribution of contamination were then analyzed and found to be a log-normal distribution with the standard deviation being a function of test area. All data for the Bryanskaya Oblast area were analyzed statistically and were adequately described by a log-normal function.« less

Photogrammetry: An available surface characterization tool for solar concentrators. Part 2: Assessment of surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shortis, M.; Johnston, G.

1997-11-01

In a previous paper, the results of photogrammetric measurements of a number of paraboloidal reflecting surfaces were presented. These results showed that photogrammetry can provide three-dimensional surface characterizations of such solar concentrators. The present paper describes the assessment of the quality of these surfaces as a derivation of the photogrammetrically produced surface coordinates. Statistical analysis of the z-coordinate distribution of errors indicates that these generally conform to a univariate Gaussian distribution, while the numerical assessment of the surface normal vectors on these surfaces indicates that the surface normal deviations appear to follow an approximately bivariate Gaussian distribution. Ray tracing ofmore » the measured surfaces to predict the expected flux distribution at the focal point of the 400 m{sup 2} dish show a close correlation with the videographically measured flux distribution at the focal point of the dish.« less

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.

1983-01-01

Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.H.

1980-01-01

Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Normal families and value distribution in connection with composite functions

NASA Astrophysics Data System (ADS)

Clifford, E. F.

2005-12-01

We prove a value distribution result which has several interesting corollaries. Let , let and let f be a transcendental entire function with order less than 1/2. Then for every nonconstant entire function g, we have that (f[circle, open]g)(k)-[alpha] has infinitely many zeros. This result also holds when k=1, for every transcendental entire function g. We also prove the following result for normal families. Let , let f be a transcendental entire function with [rho](f)<1/k, and let a0,...,ak-1,a be analytic functions in a domain [Omega]. Then the family of analytic functions g such that in [Omega], is a normal family.

Light quark Yukawa couplings from Higgs kinematics

DOE PAGES

Soreq, Yotam; Zhu, Hua Xing; Zupan, Jure

2016-12-13

We show that the normalized Higgs production p T and y h distributions are sensitive probes of Higgs couplings to light quarks. For up and/or down quark Yukawa couplings comparable to the SM b quark Yukawa themore » $$\\bar{u}u$$ or $$\\bar{d}d$$ fusion production of the Higgs could lead to appreciable softer p T distribution than in the SM. The rapidity distribution, on the other hand, becomes more forward. Here, we find that, owing partially to a downward fluctuation, one can derive competitive bounds on the two couplings using ATLAS measurements of normalized p T distribution at 8TeV. With 300 fb -1 at 13TeV LHC one could establish flavor non-universality of the Yukawa couplings in the down sector.« less

Variance stabilization and normalization for one-color microarray data using a data-driven multiscale approach.

PubMed

Motakis, E S; Nason, G P; Fryzlewicz, P; Rutter, G A

2006-10-15

Many standard statistical techniques are effective on data that are normally distributed with constant variance. Microarray data typically violate these assumptions since they come from non-Gaussian distributions with a non-trivial mean-variance relationship. Several methods have been proposed that transform microarray data to stabilize variance and draw its distribution towards the Gaussian. Some methods, such as log or generalized log, rely on an underlying model for the data. Others, such as the spread-versus-level plot, do not. We propose an alternative data-driven multiscale approach, called the Data-Driven Haar-Fisz for microarrays (DDHFm) with replicates. DDHFm has the advantage of being 'distribution-free' in the sense that no parametric model for the underlying microarray data is required to be specified or estimated; hence, DDHFm can be applied very generally, not just to microarray data. DDHFm achieves very good variance stabilization of microarray data with replicates and produces transformed intensities that are approximately normally distributed. Simulation studies show that it performs better than other existing methods. Application of DDHFm to real one-color cDNA data validates these results. The R package of the Data-Driven Haar-Fisz transform (DDHFm) for microarrays is available in Bioconductor and CRAN.

The uncertainty of nitrous oxide emissions from grazed grasslands: A New Zealand case study

NASA Astrophysics Data System (ADS)

Kelliher, Francis M.; Henderson, Harold V.; Cox, Neil R.

2017-01-01

Agricultural soils emit nitrous oxide (N2O), a greenhouse gas and the primary source of nitrogen oxides which deplete stratospheric ozone. Agriculture has been estimated to be the largest anthropogenic N2O source. In New Zealand (NZ), pastoral agriculture uses half the land area. To estimate the annual N2O emissions from NZ's agricultural soils, the nitrogen (N) inputs have been determined and multiplied by an emission factor (EF), the mass fraction of N inputs emitted as N2Osbnd N. To estimate the associated uncertainty, we developed an analytical method. For comparison, another estimate was determined by Monte Carlo numerical simulation. For both methods, expert judgement was used to estimate the N input uncertainty. The EF uncertainty was estimated by meta-analysis of the results from 185 NZ field trials. For the analytical method, assuming a normal distribution and independence of the terms used to calculate the emissions (correlation = 0), the estimated 95% confidence limit was ±57%. When there was a normal distribution and an estimated correlation of 0.4 between N input and EF, the latter inferred from experimental data involving six NZ soils, the analytical method estimated a 95% confidence limit of ±61%. The EF data from 185 NZ field trials had a logarithmic normal distribution. For the Monte Carlo method, assuming a logarithmic normal distribution for EF, a normal distribution for the other terms and independence of all terms, the estimated 95% confidence limits were -32% and +88% or ±60% on average. When there were the same distribution assumptions and a correlation of 0.4 between N input and EF, the Monte Carlo method estimated 95% confidence limits were -34% and +94% or ±64% on average. For the analytical and Monte Carlo methods, EF uncertainty accounted for 95% and 83% of the emissions uncertainty when the correlation between N input and EF was 0 and 0.4, respectively. As the first uncertainty analysis of an agricultural soils N2O emissions inventory using "country-specific" field trials to estimate EF uncertainty, this can be a potentially informative case study for the international scientific community.

Manual choice reaction times in the rate-domain

PubMed Central

Harris, Christopher M.; Waddington, Jonathan; Biscione, Valerio; Manzi, Sean

2014-01-01

Over the last 150 years, human manual reaction times (RTs) have been recorded countless times. Yet, our understanding of them remains remarkably poor. RTs are highly variable with positively skewed frequency distributions, often modeled as an inverse Gaussian distribution reflecting a stochastic rise to threshold (diffusion process). However, latency distributions of saccades are very close to the reciprocal Normal, suggesting that “rate” (reciprocal RT) may be the more fundamental variable. We explored whether this phenomenon extends to choice manual RTs. We recorded two-alternative choice RTs from 24 subjects, each with 4 blocks of 200 trials with two task difficulties (easy vs. difficult discrimination) and two instruction sets (urgent vs. accurate). We found that rate distributions were, indeed, very close to Normal, shifting to lower rates with increasing difficulty and accuracy, and for some blocks they appeared to become left-truncated, but still close to Normal. Using autoregressive techniques, we found temporal sequential dependencies for lags of at least 3. We identified a transient and steady-state component in each block. Because rates were Normal, we were able to estimate autoregressive weights using the Box-Jenkins technique, and convert to a moving average model using z-transforms to show explicit dependence on stimulus input. We also found a spatial sequential dependence for the previous 3 lags depending on whether the laterality of previous trials was repeated or alternated. This was partially dissociated from temporal dependency as it only occurred in the easy tasks. We conclude that 2-alternative choice manual RT distributions are close to reciprocal Normal and not the inverse Gaussian. This is not consistent with stochastic rise to threshold models, and we propose a simple optimality model in which reward is maximized to yield to an optimal rate, and hence an optimal time to respond. We discuss how it might be implemented. PMID:24959134

Effect of the Earth's inner structure on the gravity in definitions of height systems

NASA Astrophysics Data System (ADS)

Tenzer, Robert; Foroughi, Ismael; Pitoňák, Martin; Šprlák, Michal

2017-04-01

In context of the vertical datum unification, the geoid-to-quasi-geoid separation has been of significant interest in recent years, because most of existing local vertical datums are realized in the system of either normal or orthometric heights. Nevertheless, the normal-orthometric heights are still used in many other countries where the normal gravity values along leveling lines were adopted instead of the observed gravity. Whereas the conversion between the orthometric and normal heights is defined by means of the mean gravity disturbances (i.e. differences between the mean values of the actual and normal gravity) along the plumbline within the topography, differences between the normal and normal-orthometric heights can be described by means of the surface gravity disturbances. Since the normal gravity field does not reflect the topographic masses and actual mass density distribution inside the Earth, the definition of gravity represents a principal aspect for a realization of particular vertical datum. To address this issue in this study, we investigate effects of the Earth's inner density structure on the surface and mean gravity disturbances, and discuss their impact on the vertical datum realization. These two gravity field quantities are computed globally with a spectral resolution complete to a spherical harmonic degree 2160 using the global gravity, terrain, ice-thickness, inland bathymetry and crustal structure models. Our results reveal that both, the surface and mean gravity disturbances mostly comprise the gravitational signal of topography and masses distributed below the geoid surface. Moreover, in polar areas, a significant contribution comes from large glaciers. In contrast, the contributions of anomalous density distribution within the topography attributed to major lakes, sediments and bedrock density variations are much less pronounced. We also demonstrate that the mean gravity disturbances within the topography are significantly modified compared to the corresponding surface values mainly due to topographic elevation and terrain geometry as well as the presence of large glaciers in polar regions. Changes of the vertical gravity gradient within the topography attributed to the masses distributed below the geoid (dominated mainly by the isostatic signature and the long-wavelength gravitational signature of deep mantle density heterogeneities) are, on the other hand, relatively small. Despite differences between the normal and normal-orthometric heights could directly be assessed from the surface gravity disturbances only when taken along leveling lines with information about the spirit leveling height differences, our results indicate that differences between these two height systems can be significant.

26 CFR 1.959-4 - Distributions to United States persons not counting as dividends.

Code of Federal Regulations, 2010 CFR

2010-04-01

... normal taxes and surtaxes) of subtitle A (relating to income taxes) of the Code as a distribution which... 26 Internal Revenue 10 2010-04-01 2010-04-01 false Distributions to United States persons not... Distributions to United States persons not counting as dividends. Except as provided in section 960(a)(3) and...

Spatiotemporal analysis of Quaternary normal faults in the Northern Rocky Mountains, USA

NASA Astrophysics Data System (ADS)

Davarpanah, A.; Babaie, H. A.; Reed, P.

2010-12-01

The mid-Tertiary Basin-and-Range extensional tectonic event developed most of the normal faults that bound the ranges in the northern Rocky Mountains within Montana, Wyoming, and Idaho. The interaction of the thermally induced stress field of the Yellowstone hot spot with the existing Basin-and-Range fault blocks, during the last 15 my, has produced a new, spatially and temporally variable system of normal faults in these areas. The orientation and spatial distribution of the trace of these hot-spot induced normal faults, relative to earlier Basin-and-Range faults, have significant implications for the effect of the temporally varying and spatially propagating thermal dome on the growth of new hot spot related normal faults and reactivation of existing Basin-and-Range faults. Digitally enhanced LANDSAT 7 Enhanced Thematic Mapper Plus (ETM+) and Landsat 4 and 5 Thematic Mapper (TM) bands, with spatial resolution of 30 m, combined with analytical GIS and geological techniques helped in determining and analyzing the lineaments and traces of the Quaternary, thermally-induced normal faults in the study area. Applying the color composite (CC) image enhancement technique, the combination of bands 3, 2 and 1 of the ETM+ and TM images was chosen as the best statistical choice to create a color composite for lineament identification. The spatiotemporal analysis of the Quaternary normal faults produces significant information on the structural style, timing, spatial variation, spatial density, and frequency of the faults. The seismic Quaternary normal faults, in the whole study area, are divided, based on their age, into four specific sets, which from oldest to youngest include: Quaternary (>1.6 Ma), middle and late Quaternary (>750 ka), latest Quaternary (>15 ka), and the last 150 years. A density map for the Quaternary faults reveals that most active faults are near the current Yellowstone National Park area (YNP), where most seismically active faults, in the past 1.6 my, are located. The GIS based autocorrelation method, applied to the trace orientation, length, frequency, and spatial distribution for each age-defined fault set, revealed spatial homogeneity for each specific set. The results of the method of Moran`sI and Geary`s C show no spatial autocorrelation among the trend of the fault traces and their location. Our results suggest that while lineaments of similar age define a clustered pattern in each domain, the overall distribution pattern of lineaments with different ages seems to be non-uniform (random). The directional distribution analysis reveals a distinct range of variation for fault traces of different ages (i.e., some displaying ellipsis behavior). Among the Quaternary normal fault sets, the youngest lineament set (i.e., last 150 years) defines the greatest ellipticity (eccentricity) and the least lineaments distribution variation. The frequency rose diagram for the entire Quaternary normal faults, shows four major modes (around 360o, 330o, 300o, and 270o), and two minor modes (around 235 and 205).

A STUDY OF COGNITIVE DEVELOPMENT AND PERFORMANCE IN CHILDREN WITH NORMAL AND DEFECTIVE HEARING.

ERIC Educational Resources Information Center

TEMPLIN, MILDRED C.

A COMPARATIVE, LONGITUDINAL STUDY WAS CONDUCTED TO EXAMINE SPECIFIC PERFORMANCE CHARACTERISTICS OF DEAF AND NORMAL CHILDREN ON SELECTED COGNITIVE TASKS. THE SAMPLE, DISTRIBUTED INTO 3 AGE CATEGORIES, CONSISTED OF 72 NORMAL AND 60 DEAF CHILDREN. MEASURES WERE SELECTED TO ASSESS THE PERFORMANCE OF SUBJECTS (1) IN DIFFERENT AREAS OF COGNITION, (2) BY…

Multiple Regression with Varying Levels of Correlation among Predictors: Monte Carlo Sampling from Normal and Non-Normal Populations.

ERIC Educational Resources Information Center

Vasu, Ellen Storey

1978-01-01

The effects of the violation of the assumption of normality in the conditional distributions of the dependent variable, coupled with the condition of multicollinearity upon the outcome of testing the hypothesis that the regression coefficient equals zero, are investigated via a Monte Carlo study. (Author/JKS)

The Distribution of Fixation Durations during Reading: Effects of Stimulus Quality

ERIC Educational Resources Information Center

White, Sarah J.; Staub, Adrian

2012-01-01

Participants' eye movements were recorded as they read single sentences presented normally, presented entirely in faint text, or presented normally except for a single faint word. Fixations were longer when the entire sentence was faint than when the sentence was presented normally. In addition, fixations were much longer on a single faint word…

Discrim: a computer program using an interactive approach to dissect a mixture of normal or lognormal distributions

USGS Publications Warehouse

Bridges, N.J.; McCammon, R.B.

1980-01-01

DISCRIM is an interactive computer graphics program that dissects mixtures of normal or lognormal distributions. The program was written in an effort to obtain a more satisfactory solution to the dissection problem than that offered by a graphical or numerical approach alone. It combines graphic and analytic techniques using a Tektronix1 terminal in a time-share computing environment. The main program and subroutines were written in the FORTRAN language. ?? 1980.

Analysis of domestic refrigerator temperatures and home storage time distributions for shelf-life studies and food safety risk assessment.

PubMed

Roccato, Anna; Uyttendaele, Mieke; Membré, Jeanne-Marie

2017-06-01

In the framework of food safety, when mimicking the consumer phase, the storage time and temperature used are mainly considered as single point estimates instead of probability distributions. This singlepoint approach does not take into account the variability within a population and could lead to an overestimation of the parameters. Therefore, the aim of this study was to analyse data on domestic refrigerator temperatures and storage times of chilled food in European countries in order to draw general rules which could be used either in shelf-life testing or risk assessment. In relation to domestic refrigerator temperatures, 15 studies provided pertinent data. Twelve studies presented normal distributions, according to the authors or from the data fitted into distributions. Analysis of temperature distributions revealed that the countries were separated into two groups: northern European countries and southern European countries. The overall variability of European domestic refrigerators is described by a normal distribution: N (7.0, 2.7)°C for southern countries, and, N (6.1, 2.8)°C for the northern countries. Concerning storage times, seven papers were pertinent. Analysis indicated that the storage time was likely to end in the first days or weeks (depending on the product use-by-date) after purchase. Data fitting showed the exponential distribution was the most appropriate distribution to describe the time that food spent at consumer's place. The storage time was described by an exponential distribution corresponding to the use-by date period divided by 4. In conclusion, knowing that collecting data is time and money consuming, in the absence of data, and at least for the European market and for refrigerated products, building a domestic refrigerator temperature distribution using a Normal law and a time-to-consumption distribution using an Exponential law would be appropriate. Copyright © 2017 Elsevier Ltd. All rights reserved.

Drought forecasting in Luanhe River basin involving climatic indices

NASA Astrophysics Data System (ADS)

Ren, Weinan; Wang, Yixuan; Li, Jianzhu; Feng, Ping; Smith, Ronald J.

2017-11-01

Drought is regarded as one of the most severe natural disasters globally. This is especially the case in Tianjin City, Northern China, where drought can affect economic development and people's livelihoods. Drought forecasting, the basis of drought management, is an important mitigation strategy. In this paper, we evolve a probabilistic forecasting model, which forecasts transition probabilities from a current Standardized Precipitation Index (SPI) value to a future SPI class, based on conditional distribution of multivariate normal distribution to involve two large-scale climatic indices at the same time, and apply the forecasting model to 26 rain gauges in the Luanhe River basin in North China. The establishment of the model and the derivation of the SPI are based on the hypothesis of aggregated monthly precipitation that is normally distributed. Pearson correlation and Shapiro-Wilk normality tests are used to select appropriate SPI time scale and large-scale climatic indices. Findings indicated that longer-term aggregated monthly precipitation, in general, was more likely to be considered normally distributed and forecasting models should be applied to each gauge, respectively, rather than to the whole basin. Taking Liying Gauge as an example, we illustrate the impact of the SPI time scale and lead time on transition probabilities. Then, the controlled climatic indices of every gauge are selected by Pearson correlation test and the multivariate normality of SPI, corresponding climatic indices for current month and SPI 1, 2, and 3 months later are demonstrated using Shapiro-Wilk normality test. Subsequently, we illustrate the impact of large-scale oceanic-atmospheric circulation patterns on transition probabilities. Finally, we use a score method to evaluate and compare the performance of the three forecasting models and compare them with two traditional models which forecast transition probabilities from a current to a future SPI class. The results show that the three proposed models outperform the two traditional models and involving large-scale climatic indices can improve the forecasting accuracy.

Using Computer Graphics in Statistics.

ERIC Educational Resources Information Center

Kerley, Lyndell M.

1990-01-01

Described is software which allows a student to use simulation to produce analytical output as well as graphical results. The results include a frequency histogram of a selected population distribution, a frequency histogram of the distribution of the sample means, and test the normality distributions of the sample means. (KR)

Using Extreme Groups Strategy When Measures Are Not Normally Distributed.

ERIC Educational Resources Information Center

Fowler, Robert L.

1992-01-01

A Monte Carlo simulation explored how to optimize power in the extreme groups strategy when sampling from nonnormal distributions. Results show that the optimum percent for the extreme group selection was approximately the same for all population shapes, except the extremely platykurtic (uniform) distribution. (SLD)

Evaluation of Mean and Variance Integrals without Integration

ERIC Educational Resources Information Center

Joarder, A. H.; Omar, M. H.

2007-01-01

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

Estimating insect flight densities from attractive trap catches and flight height distributions

USDA-ARS?s Scientific Manuscript database

Insect species often exhibit a specific mean flight height and vertical flight distribution that approximates a normal distribution with a characteristic standard deviation (SD). Many studies in the literature report catches on passive (non-attractive) traps at several heights. These catches were us...

Physics of collisionless scrape-off-layer plasma during normal and off-normal Tokamak operating conditions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hassanein, A.; Konkashbaev, I.

1999-03-15

The structure of a collisionless scrape-off-layer (SOL) plasma in tokamak reactors is being studied to define the electron distribution function and the corresponding sheath potential between the divertor plate and the edge plasma. The collisionless model is shown to be valid during the thermal phase of a plasma disruption, as well as during the newly desired low-recycling normal phase of operation with low-density, high-temperature, edge plasma conditions. An analytical solution is developed by solving the Fokker-Planck equation for electron distribution and balance in the SOL. The solution is in good agreement with numerical studies using Monte-Carlo methods. The analytical solutionsmore » provide an insight to the role of different physical and geometrical processes in a collisionless SOL during disruptions and during the enhanced phase of normal operation over a wide range of parameters.« less

Optimum runway orientation relative to crosswinds

NASA Technical Reports Server (NTRS)

Falls, L. W.; Brown, S. C.

1972-01-01

Specific magnitudes of crosswinds may exist that could be constraints to the success of an aircraft mission such as the landing of the proposed space shuttle. A method is required to determine the orientation or azimuth of the proposed runway which will minimize the probability of certain critical crosswinds. Two procedures for obtaining the optimum runway orientation relative to minimizing a specified crosswind speed are described and illustrated with examples. The empirical procedure requires only hand calculations on an ordinary wind rose. The theoretical method utilizes wind statistics computed after the bivariate normal elliptical distribution is applied to a data sample of component winds. This method requires only the assumption that the wind components are bivariate normally distributed. This assumption seems to be reasonable. Studies are currently in progress for testing wind components for bivariate normality for various stations. The close agreement between the theoretical and empirical results for the example chosen substantiates the bivariate normal assumption.

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

Simulations of large acoustic scintillations in the straits of Florida.

PubMed

Tang, Xin; Tappert, F D; Creamer, Dennis B

2006-12-01

Using a full-wave acoustic model, Monte Carlo numerical studies of intensity fluctuations in a realistic shallow water environment that simulates the Straits of Florida, including internal wave fluctuations and bottom roughness, have been performed. Results show that the sound intensity at distant receivers scintillates dramatically. The acoustic scintillation index SI increases rapidly with propagation range and is significantly greater than unity at ranges beyond about 10 km. This result supports a theoretical prediction by one of the authors. Statistical analyses show that the distribution of intensity of the random wave field saturates to the expected Rayleigh distribution with SI= 1 at short range due to multipath interference effects, and then SI continues to increase to large values. This effect, which is denoted supersaturation, is universal at long ranges in waveguides having lossy boundaries (where there is differential mode attenuation). The intensity distribution approaches a log-normal distribution to an excellent approximation; it may not be a universal distribution and comparison is also made to a K distribution. The long tails of the log-normal distribution cause "acoustic intermittency" in which very high, but rare, intensities occur.

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Altered newborn gender distribution in patients with low mid-trimester maternal serum human chorionic gonadotropin (MShCG).

PubMed

Santolaya-Forgas, J; Meyer, W J; Burton, B K; Scommegna, A

1997-01-01

to determine if the sex ratio (male/female) is altered in infants born to patients with low mid-trimester maternal serum human chorionic gonadotropin (MShCG). Between 2/1/90 and 1/3/91, 3,116 patients underwent prenatal screening using second-trimester maternal serum alpha-fetoprotein (MSAFP), MShCG, and maternal serum unconjugated estriol (MSuE3). Among these, there were 132 patients with low second-trimester MShCG (< 0.4 MoM), normal MSAFP and MSuE3. The gender distribution of these term, normal newborns was compared to that of 237 controls, matched for race, maternal age, and referral source and delivered at term to mothers with normal mid-trimester MSAFP, MSuE3, and MShCG. The gender distribution of these two groups of newborns was also compared to that of 78 term newborns from the same obstetrical population delivered to mothers with second-trimester MShCG > 2.5 MoM and normal MSAFP and MSuE3. All patients had a complete obstetrical history. Forty-nine percent of the controls were male vs. 62% of the group with slow second-trimester MShCG (P < .01). Within the group with low MShCG, 59% of infants were male when the MShCG was between 0.19 and 0.4 MoM (A) and 80% when the MShCG was < 0.2 MoM (B) (control vs. A vs. B P < .005). The sex ratio in the high-MShCG group was similar to control. The data suggest that gender distribution is different from normal in patients with low mid-trimester MShCG.

3D modeling of effects of increased oxygenation and activity concentration in tumors treated with radionuclides and antiangiogenic drugs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lagerloef, Jakob H.; Kindblom, Jon; Bernhardt, Peter

Purpose: Formation of new blood vessels (angiogenesis) in response to hypoxia is a fundamental event in the process of tumor growth and metastatic dissemination. However, abnormalities in tumor neovasculature often induce increased interstitial pressure (IP) and further reduce oxygenation (pO{sub 2}) of tumor cells. In radiotherapy, well-oxygenated tumors favor treatment. Antiangiogenic drugs may lower IP in the tumor, improving perfusion, pO{sub 2} and drug uptake, by reducing the number of malfunctioning vessels in the tissue. This study aims to create a model for quantifying the effects of altered pO{sub 2}-distribution due to antiangiogenic treatment in combination with radionuclide therapy. Methods:more » Based on experimental data, describing the effects of antiangiogenic agents on oxygenation of GlioblastomaMultiforme (GBM), a single cell based 3D model, including 10{sup 10} tumor cells, was developed, showing how radionuclide therapy response improves as tumor oxygenation approaches normal tissue levels. The nuclides studied were {sup 90}Y, {sup 131}I, {sup 177}Lu, and {sup 211}At. The absorbed dose levels required for a tumor control probability (TCP) of 0.990 are compared for three different log-normal pO{sub 2}-distributions: {mu}{sub 1} = 2.483, {sigma}{sub 1} = 0.711; {mu}{sub 2} = 2.946, {sigma}{sub 2} = 0.689; {mu}{sub 3} = 3.689, and {sigma}{sub 3} = 0.330. The normal tissue absorbed doses will, in turn, depend on this. These distributions were chosen to represent the expected oxygen levels in an untreated hypoxic tumor, a hypoxic tumor treated with an anti-VEGF agent, and in normal, fully-oxygenated tissue, respectively. The former two are fitted to experimental data. The geometric oxygen distributions are simulated using two different patterns: one Monte Carlo based and one radially increasing, while keeping the log-normal volumetric distributions intact. Oxygen and activity are distributed, according to the same pattern. Results: As tumor pO{sub 2} approaches normal tissue levels, the therapeutic effect is improved so that the normal tissue absorbed doses can be decreased by more than 95%, while retaining TCP, in the most favorable scenario and by up to about 80% with oxygen levels previously achieved in vivo, when the least favourable oxygenation case is used as starting point. The major difference occurs in poorly oxygenated cells. This is also where the pO{sub 2}-dependence of the oxygen enhancement ratio is maximal. Conclusions: Improved tumor oxygenation together with increased radionuclide uptake show great potential for optimising treatment strategies, leaving room for successive treatments, or lowering absorbed dose to normal tissues, due to increased tumor response. Further studies of the concomitant use of antiangiogenic drugs and radionuclide therapy therefore appear merited.« less

Accumulation risk assessment for the flooding hazard

NASA Astrophysics Data System (ADS)

Roth, Giorgio; Ghizzoni, Tatiana; Rudari, Roberto

2010-05-01

One of the main consequences of the demographic and economic development and of markets and trades globalization is represented by risks cumulus. In most cases, the cumulus of risks intuitively arises from the geographic concentration of a number of vulnerable elements in a single place. For natural events, risks cumulus can be associated, in addition to intensity, also to event's extension. In this case, the magnitude can be such that large areas, that may include many regions or even large portions of different countries, are stroked by single, catastrophic, events. Among natural risks, the impact of the flooding hazard cannot be understated. To cope with, a variety of mitigation actions can be put in place: from the improvement of monitoring and alert systems to the development of hydraulic structures, throughout land use restrictions, civil protection, financial and insurance plans. All of those viable options present social and economic impacts, either positive or negative, whose proper estimate should rely on the assumption of appropriate - present and future - flood risk scenarios. It is therefore necessary to identify proper statistical methodologies, able to describe the multivariate aspects of the involved physical processes and their spatial dependence. In hydrology and meteorology, but also in finance and insurance practice, it has early been recognized that classical statistical theory distributions (e.g., the normal and gamma families) are of restricted use for modeling multivariate spatial data. Recent research efforts have been therefore directed towards developing statistical models capable of describing the forms of asymmetry manifest in data sets. This, in particular, for the quite frequent case of phenomena whose empirical outcome behaves in a non-normal fashion, but still maintains some broad similarity with the multivariate normal distribution. Fruitful approaches were recognized in the use of flexible models, which include the normal distribution as a special or limiting case (e.g., the skew-normal or skew-t distributions). The present contribution constitutes an attempt to provide a better estimation of the joint probability distribution able to describe flood events in a multi-site multi-basin fashion. This goal will be pursued through the multivariate skew-t distribution, which allows to analytically define the joint probability distribution. Performances of the skew-t distribution will be discussed with reference to the Tanaro River in Northwestern Italy. To enhance the characteristics of the correlation structure, both nested and non-nested gauging stations will be selected, with significantly different contributing areas.

The social architecture of capitalism

NASA Astrophysics Data System (ADS)

Wright, Ian

2005-02-01

A dynamic model of the social relations between workers and capitalists is introduced. The model self-organises into a dynamic equilibrium with statistical properties that are in close qualitative and in many cases quantitative agreement with a broad range of known empirical distributions of developed capitalism, including the power-law firm size distribution, the Laplace firm and GDP growth distribution, the lognormal firm demises distribution, the exponential recession duration distribution, the lognormal-Pareto income distribution, and the gamma-like firm rate-of-profit distribution. Normally these distributions are studied in isolation, but this model unifies and connects them within a single causal framework. The model also generates business cycle phenomena, including fluctuating wage and profit shares in national income about values consistent with empirical studies. The generation of an approximately lognormal-Pareto income distribution and an exponential-Pareto wealth distribution demonstrates that the power-law regime of the income distribution can be explained by an additive process on a power-law network that models the social relation between employers and employees organised in firms, rather than a multiplicative process that models returns to investment in financial markets. A testable consequence of the model is the conjecture that the rate-of-profit distribution is consistent with a parameter-mix of a ratio of normal variates with means and variances that depend on a firm size parameter that is distributed according to a power-law.

Power of tests of normality for detecting contaminated normal samples

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thode, H.C. Jr.; Smith, L.A.; Finch, S.J.

1981-01-01

Seventeen tests of normality or goodness of fit were evaluated for power at detecting a contaminated normal sample. This study used 1000 replications each of samples of size 12, 17, 25, 33, 50, and 100 from six different contaminated normal distributions. The kurtosis test was the most powerful over all sample sizes and contaminations. The Hogg and weighted Kolmogorov-Smirnov tests were second. The Kolmogorov-Smirnov, chi-squared, Anderson-Darling, and Cramer-von-Mises tests had very low power at detecting contaminated normal random variables. Tables of the power of the tests and the power curves of certain tests are given.

Influence of weight and body fat distribution on bone density in postmenopausal women.

PubMed

Murillo-Uribe, A; Carranza-Lira, S; Martínez-Trejo, N; Santos-González, J

2000-01-01

To determine whether obesity or body fat distribution induces a greater modification on bone remodeling biochemistry (BRB) and bone density in postmenopausal women. One hundred and thirteen postmenopausal patients were studied. They were initially divided according to body mass index (BMI), and afterwards by waist-hip ratio (WHR) as well as combinations of the two factors. Hormone measurements and assessments of BRB were also done. Dual-emission X-ray absorptiometry from the lumbar column and hip was performed with Lunar DPXL equipment, and the standard deviation in relation to young adult (T) and age-matched subjects (Z) was calculated. Statistical analysis was done by the Mann-Whitney U test. The relation of BMI and WHR with the variables was calculated by simple regression analysis. When divided according to BMI, there was greater bone density in the femoral neck in those with normal weight. After dividing according to WHR, the Z scores had a trend to a lesser decrease in those with upper level body fat distribution. Divided according to BMI and WHR, obese patients with upper-level body fat distribution had greater bone density in the lumbar column than those with normal weight and lower-level body fat distribution. With the same WHR, those with normal weight had greater bone density than those who were obese. A beneficial effect of upper-level body fat distribution on bone density was found. It is greater than that from obesity alone, and obesity and upper-level body fat distribution have an additive effect on bone density.

Determination of statistics for any rotation of axes of a bivariate normal elliptical distribution. [of wind vector components

NASA Technical Reports Server (NTRS)

Falls, L. W.; Crutcher, H. L.

1976-01-01

Transformation of statistics from a dimensional set to another dimensional set involves linear functions of the original set of statistics. Similarly, linear functions will transform statistics within a dimensional set such that the new statistics are relevant to a new set of coordinate axes. A restricted case of the latter is the rotation of axes in a coordinate system involving any two correlated random variables. A special case is the transformation for horizontal wind distributions. Wind statistics are usually provided in terms of wind speed and direction (measured clockwise from north) or in east-west and north-south components. A direct application of this technique allows the determination of appropriate wind statistics parallel and normal to any preselected flight path of a space vehicle. Among the constraints for launching space vehicles are critical values selected from the distribution of the expected winds parallel to and normal to the flight path. These procedures are applied to space vehicle launches at Cape Kennedy, Florida.

Anomalous Transient Amplification of Waves in Non-normal Photonic Media

NASA Astrophysics Data System (ADS)

Makris, K. G.; Ge, L.; Türeci, H. E.

2014-10-01

Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally been the mitigation of optical losses. Recent work has shown that a new class of optical materials that consist of a precisely balanced distribution of loss and gain can be exploited to engineer novel functionalities for propagating and filtering electromagnetic radiation. Here we show a generic property of optical systems that feature an unbalanced distribution of loss and gain, described by non-normal operators, namely, that an overall lossy optical system can transiently amplify certain input signals by several orders of magnitude. We present a mathematical framework to analyze the dynamics of wave propagation in media with an arbitrary distribution of loss and gain, and we construct the initial conditions to engineer such non-normal power amplifiers. Our results point to a new design space for engineered optical systems employed in photonics and quantum optics.

Neutron monitor generated data distributions in quantum variational Monte Carlo

NASA Astrophysics Data System (ADS)

Kussainov, A. S.; Pya, N.

2016-08-01

We have assessed the potential applications of the neutron monitor hardware as random number generator for normal and uniform distributions. The data tables from the acquisition channels with no extreme changes in the signal level were chosen as the retrospective model. The stochastic component was extracted by fitting the raw data with splines and then subtracting the fit. Scaling the extracted data to zero mean and variance of one is sufficient to obtain a stable standard normal random variate. Distributions under consideration pass all available normality tests. Inverse transform sampling is suggested to use as a source of the uniform random numbers. Variational Monte Carlo method for quantum harmonic oscillator was used to test the quality of our random numbers. If the data delivery rate is of importance and the conventional one minute resolution neutron count is insufficient, we could always settle for an efficient seed generator to feed into the faster algorithmic random number generator or create a buffer.

Shape model of the maxillary dental arch using Fourier descriptors with an application in the rehabilitation for edentulous patient.

PubMed

Rijal, Omar M; Abdullah, Norli A; Isa, Zakiah M; Noor, Norliza M; Tawfiq, Omar F

2013-01-01

The knowledge of teeth positions on the maxillary arch is useful in the rehabilitation of the edentulous patient. A combination of angular (θ), and linear (l) variables representing position of four teeth were initially proposed as the shape descriptor of the maxillary dental arch. Three categories of shape were established, each having a multivariate normal distribution. It may be argued that 4 selected teeth on the standardized digital images of the dental casts could be considered as insufficient with respect to representing shape. However, increasing the number of points would create problems with dimensions and proof of existence of the multivariate normal distribution is extremely difficult. This study investigates the ability of Fourier descriptors (FD) using all maxillary teeth to find alternative shape models. Eight FD terms were sufficient to represent 21 points on the arch. Using these 8 FD terms as an alternative shape descriptor, three categories of shape were verified, each category having the complex normal distribution.

Psychological Health and Overweight and Obesity Among High Stressed Work Environments

PubMed Central

Faghri, Pouran D; Mignano, Christina; Huedo- Medina, Tania B; Cherniack, Martin

2016-01-01

Correctional employees are recognized to underreport stress and stress symptoms and are known to have a culture that discourages appearing “weak” and seeking psychiatric help. This study assesses underreporting of stress and emotions. Additionally, it evaluates the relationships between stress and emotions on health behaviors. Correctional employees (n=317) completed physical assessments to measure body mass index (BMI), and surveys to assess perceived stress, emotions, and health behavior (diet, exercise, and sleep quality). Stress and emotion survey items were evaluated for under-reporting via skewness, kurtosis, and visual assessment of histograms. Structural equation modeling evaluated relationships between stress/emotion and health behaviors. Responses to stress and negatively worded emotions were non-normally distributed whereas responses to positively-worded emotions were normally distributed. Emotion predicted diet, exercise, and sleep quality whereas stress predicted only sleep quality. As stress was a poor predictor of health behaviors and responses to stress and negatively worded emotions were non-normally distributed it may suggests correctional employees are under-reporting stress and negative emotions. PMID:27547828

Psychological Health and Overweight and Obesity Among High Stressed Work Environments.

PubMed

Faghri, Pouran D; Mignano, Christina; Huedo-Medina, Tania B; Cherniack, Martin

2015-07-01

Correctional employees are recognized to underreport stress and stress symptoms and are known to have a culture that discourages appearing "weak" and seeking psychiatric help. This study assesses underreporting of stress and emotions. Additionally, it evaluates the relationships between stress and emotions on health behaviors. Correctional employees (n=317) completed physical assessments to measure body mass index (BMI), and surveys to assess perceived stress, emotions, and health behavior (diet, exercise, and sleep quality). Stress and emotion survey items were evaluated for under-reporting via skewness, kurtosis, and visual assessment of histograms. Structural equation modeling evaluated relationships between stress/emotion and health behaviors. Responses to stress and negatively worded emotions were non-normally distributed whereas responses to positively-worded emotions were normally distributed. Emotion predicted diet, exercise, and sleep quality whereas stress predicted only sleep quality. As stress was a poor predictor of health behaviors and responses to stress and negatively worded emotions were non-normally distributed it may suggests correctional employees are under-reporting stress and negative emotions.

Atlas-derived perfusion correlates of white matter hyperintensities in patients with reduced cardiac output.

PubMed

Jefferson, Angela L; Holland, Christopher M; Tate, David F; Csapo, Istvan; Poppas, Athena; Cohen, Ronald A; Guttmann, Charles R G

2011-01-01

Reduced cardiac output is associated with increased white matter hyperintensities (WMH) and executive dysfunction in older adults, which may be secondary to relations between systemic and cerebral perfusion. This study preliminarily describes the regional distribution of cerebral WMH in the context of a normal cerebral perfusion atlas and aims to determine if these variables are associated with reduced cardiac output. Thirty-two participants (72 ± 8 years old, 38% female) with cardiovascular risk factors or disease underwent structural MRI acquisition at 1.5T using a standard imaging protocol that included FLAIR sequences. WMH distribution was examined in common anatomical space using voxel-based morphometry and as a function of normal cerebral perfusion patterns by overlaying a single photon emission computed tomography (SPECT) atlas. Doppler echocardiogram data was used to dichotomize the participants on the basis of low (n=9) and normal (n=23) cardiac output. Global WMH count and volume did not differ between the low and normal cardiac output groups; however, atlas-derived SPECT perfusion values in regions of hyperintensities were reduced in the low versus normal cardiac output group (p<0.001). Our preliminary data suggest that participants with low cardiac output have WMH in regions of relatively reduced perfusion, while normal cardiac output participants have WMH in regions with relatively higher regional perfusion. This spatial perfusion distribution difference for areas of WMH may occur in the context of reduced systemic perfusion, which subsequently impacts cerebral perfusion and contributes to subclinical or clinical microvascular damage. Copyright © 2009 Elsevier Inc. All rights reserved.

Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis.

PubMed

Bishara, Anthony J; Li, Jiexiang; Nash, Thomas

2018-02-01

When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z' under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z' interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non-parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods (PM1 and HC4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta-analysis. Supporting information includes R code. © 2017 The British Psychological Society.

Determining Normal-Distribution Tolerance Bounds Graphically

NASA Technical Reports Server (NTRS)

Mezzacappa, M. A.

1983-01-01

Graphical method requires calculations and table lookup. Distribution established from only three points: mean upper and lower confidence bounds and lower confidence bound of standard deviation. Method requires only few calculations with simple equations. Graphical procedure establishes best-fit line for measured data and bounds for selected confidence level and any distribution percentile.

Conormal distributions in the Shubin calculus of pseudodifferential operators

NASA Astrophysics Data System (ADS)

Cappiello, Marco; Schulz, René; Wahlberg, Patrik

2018-02-01

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.

14 CFR 23.1445 - Oxygen distribution system.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Oxygen distribution system. 23.1445 Section... Equipment § 23.1445 Oxygen distribution system. (a) Except for flexible lines from oxygen outlets to the... used for any oxygen line that is normally pressurized during flight. (b) Nonmetallic oxygen...

14 CFR 23.1445 - Oxygen distribution system.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Oxygen distribution system. 23.1445 Section... Equipment § 23.1445 Oxygen distribution system. (a) Except for flexible lines from oxygen outlets to the... used for any oxygen line that is normally pressurized during flight. (b) Nonmetallic oxygen...

14 CFR 23.1445 - Oxygen distribution system.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Oxygen distribution system. 23.1445 Section... Equipment § 23.1445 Oxygen distribution system. (a) Except for flexible lines from oxygen outlets to the... used for any oxygen line that is normally pressurized during flight. (b) Nonmetallic oxygen...

14 CFR 23.1445 - Oxygen distribution system.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Oxygen distribution system. 23.1445 Section... Equipment § 23.1445 Oxygen distribution system. (a) Except for flexible lines from oxygen outlets to the... used for any oxygen line that is normally pressurized during flight. (b) Nonmetallic oxygen...

49 CFR 192.195 - Protection against accidental overpressuring.

Code of Federal Regulations, 2010 CFR

2010-10-01

... of §§ 192.199 and 192.201. (b) Additional requirements for distribution systems. Each distribution..., load, and other service conditions that will be experienced in normal operation of the system, and that...

Stochastic Modeling Approach to the Incubation Time of Prionic Diseases

NASA Astrophysics Data System (ADS)

Ferreira, A. S.; da Silva, M. A.; Cressoni, J. C.

2003-05-01

Transmissible spongiform encephalopathies are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrPSc) form and the host-encoded (PrPC) conformation, in a kind of autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE (bovine spongiform encephalopathy) data very well. Computer simulation results also yield the correct BSE incubation time distribution at low PrPC densities.

Cortical Iron Reflects Severity of Alzheimer’s Disease

PubMed Central

van Duijn, Sara; Bulk, Marjolein; van Duinen, Sjoerd G.; Nabuurs, Rob J.A.; van Buchem, Mark A.; van der Weerd, Louise; Natté, Remco

2017-01-01

Abnormal iron distribution in the isocortex is increasingly recognized as an in vivo marker for Alzheimer’s disease (AD). However, the contribution of iron accumulation to the AD pathology is still poorly understood. In this study, we investigated: 1) frontal cortical iron distribution in AD and normal aging and 2) the relation between iron distribution and degree of AD pathology. We used formalin fixed paraffin embedded frontal cortex from 10 AD patients, 10 elder, 10 middle aged, and 10 young controls and visualized iron with a modified Perl’s histochemical procedure. AD and elderly subjects were not different with respect to age and sex distribution. Iron distribution in the frontal cortex was not affected by normal aging but was clearly different between AD and controls. AD showed accumulation of iron in plaques, activated microglia, and, in the most severe cases, in the mid-cortical layers along myelinated fibers. The degree of altered iron accumulations was correlated to the amount of amyloid-β plaques and tau pathology in the same block, as well as to Braak stage (p < 0.001). AD and normal aging show different iron and myelin distribution in frontal cortex. These changes appear to occur after the development of the AD pathological hallmarks. These findings may help the interpretation of high resolution in vivo MRI and suggest the potential of using changes in iron-based MRI contrast to indirectly determine the degree of AD pathology in the frontal cortex. PMID:29081415

Comparison of 68Ga- and fluorescence-labeled microspheres for measurement of relative pulmonary perfusion in anesthetized pigs.

PubMed

Braune, Anja; Scharffenberg, Martin; Naumann, Anne; Bluth, Thomas; de Abreu, Marcelo Gama; Kotzerke, Jörg

2018-06-01

We compared 68 Gallium ( 68 Ga)- and fluorescence-labeled microspheres for measurement of pulmonary perfusion distribution in anesthetized pigs without lung injury. In two mechanically ventilated pigs, the distribution of pulmonary perfusion was marked in vivo with 68 Ga- and fluorescence-labeled microspheres in supine and prone position. After each injection, the distribution of 68 Ga-labeled microspheres was measured in vivo with positron emission tomography/ computed tomography (PET/CT) in the position in which microspheres were injected and vice versa. The distribution of fluorescence-labeled microspheres was measured ex vivo . Perfusion distributions were compared between methods and postures within four lung regions and along the ventro-dorsal gradient. After each injection of 68 Ga-labeled microspheres, changes in ventro-dorsal perfusion gradients induced by repositioning were compared for volume- and mass-normalized PET/CT measurements. Regional and gradient analyses of in vivo and ex vivo measurements, respectively, consistently revealed higher pulmonary perfusion in dorsal than ventral regions in supine positioned animals. Both methods showed more pronounced perfusion gradients in supine compared to prone position. Changes in animal position were associated with alterations in the ventro-dorsal perfusion gradient when volume-, but not mass-normalization was conducted for PET/CT data. Ex vivo fluorescence- and in vivo 68 Ga-labeled microspheres measurements revealed similar perfusion distributions. Mass-normalized perfusion measurements by 68 Ga-labeled microspheres and PET/CT were not affected by positioning artifacts. Schattauer GmbH.

Distribution of Different Sized Ocular Surface Vessels in Diabetics and Normal Individuals.

PubMed

Banaee, Touka; Pourreza, Hamidreza; Doosti, Hassan; Abrishami, Mojtaba; Ehsaei, Asieh; Basiry, Mohsen; Pourreza, Reza

2017-01-01

To compare the distribution of different sized vessels using digital photographs of the ocular surface of diabetic and normal individuals. In this cross-sectional study, red-free conjunctival photographs of diabetic and normal individuals, aged 30-60 years, were taken under defined conditions and analyzed using a Radon transform-based algorithm for vascular segmentation. The image areas occupied by vessels (AOV) of different diameters were calculated. The main outcome measure was the distribution curve of mean AOV of different sized vessels. Secondary outcome measures included total AOV and standard deviation (SD) of AOV of different sized vessels. Two hundred and sixty-eight diabetic patients and 297 normal (control) individuals were included, differing in age (45.50 ± 5.19 vs. 40.38 ± 6.19 years, P < 0.001), systolic (126.37 ± 20.25 vs. 119.21 ± 15.81 mmHg, P < 0.001) and diastolic (78.14 ± 14.21 vs. 67.54 ± 11.46 mmHg, P < 0.001) blood pressures. The distribution curves of mean AOV differed between patients and controls (smaller AOV for larger vessels in patients; P < 0.001) as well as between patients without retinopathy and those with non-proliferative diabetic retinopathy (NPDR); with larger AOV for smaller vessels in NPDR ( P < 0.001). Controlling for the effect of confounders, patients had a smaller total AOV, larger total SD of AOV, and a more skewed distribution curve of vessels compared to controls. Presence of diabetes mellitus is associated with contraction of larger vessels in the conjunctiva. Smaller vessels dilate with diabetic retinopathy. These findings may be useful in the photographic screening of diabetes mellitus and retinopathy.

Cellular Location and Expression of Na+, K+-ATPase α Subunits Affect the Anti-Proliferative Activity of Oleandrin

PubMed Central

Yang, Peiying; Cartwright, Carrie; Efuet, Ekem; Hamilton, Stanley R.; Wistuba, Ignacio Ivan; Menter, David; Addington, Crandell; Shureiqi, Imad; Newman, Robert A.

2015-01-01

The purpose of this study was to investigate whether intracellular distribution of Na+, K+-ATPase α3 subunit, a receptor for cardiac glycosides including oleandrin, is differentially altered in cancer versus normal cells and whether this altered distribution can be therapeutically targeted to inhibit cancer cell survival. The cellular distribution of Na+, K+-ATPase α3 isoform was investigated in paired normal and cancerous mucosa biopsy samples from patients with lung and colorectal cancers by immunohistochemical staining. The effects of oleandrin on α3 subunit intracellular distribution, cell death, proliferation, and EKR phosphorylation were examined in differentiated and undifferentiated human colon cancer CaCO-2 cells. While Na+, K+-ATPase α3 isoform was predominantly located near the cytoplasmic membrane in normal human colon and lung epithelia, the expression of this subunit in their paired cancer epithelia was shifted to a peri-nuclear position in both a qualitative and quantitative manner. Similarly, distribution of α3 isoform was also shifted from a cytoplasmic membrane location in differentiated human colon cancer CaCO-2 cells to a peri-nuclear position in undifferentiated CaCO-2 cells. Intriguingly, oleandrin exerted threefold stronger anti-proliferative activity in undifferentiated CaCO-2 cells (IC50, 8.25 nM) than in differentiated CaCO-2 cells (IC50, >25 nM). Oleandrin (10 to 20 nM) caused an autophagic cell death and altered ERK phosphorylation in undifferentiated but not in differentiated CaCO-2 cells. These data demonstrate that the intracellular location of Na+, K+-ATPase α3 isoform is altered in human cancer versus normal cells. These changes in α3 cellular location and abundance may indicate a potential target of opportunity for cancer therapy. PMID:23073998

Beyond the power law: Uncovering stylized facts in interbank networks

NASA Astrophysics Data System (ADS)

Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen

2015-06-01

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.

Intracellular distribution of Photofrin in malignant and normal endothelial cell lines.

PubMed

Saczko, J; Mazurkiewicz, M; Chwiłkowska, A; Kulbacka, J; Kramer, G; Ługowski, M; Snietura, M; Banaś, T

2007-01-01

Compared to current treatments including surgery, radiation therapy, and chemotherapy, PDT offers the advantage of an effective and selective method of destroying diseased tissues without damaging surrounding healthy tissues. One of the aspects of antitumour effectiveness of PDT is related to the distribution of photosensitizing drugs. The localization of photosensitizers in cytoplasmic organelles during PDT plays a major role in the cell destruction; therefore, intracellular localization of Ph in malignant and normal cells was investigated. The cell lines used throughout the study were: human malignant A549, MCF-7, Me45 and normal endothelial cell line HUV-EC-C. After incubation with Ph cells were examined using fluorescence and confocal microscopy to visualize the photosensitizer accumulation. For cytoplasm and mitochondria identification, cells were stained with CellTracker Green and MitoTracker Green, respectively. Distribution of Ph was different in malignant and normal cells and dependent on the incubation time. The maximal concentration of Ph in two malignant cell lines (A549 and MCF-7) was observed after 4 hours of incubation, and the most intensive signal was observed around the nuclear envelope. Intracellular distribution of Ph in the Me45 cell line showed that the fluorescence emitted by Ph overlaid that from MitoTracker. This indicates preferential accumulation of the sensitizer in mitochondria. Our results based on the mitochondrial localization support the idea that PDT can contribute to elimination of malignant cells by inducing apoptosis, which is of physiological significance.

Logistics Management Systems in Desert Shield/Desert Storm - How Well Did They Do?

DTIC Science & Technology

1992-04-07

were grovped into five major categories: Containerization and Packaging; Distribution Management ; Automation/Communications; Peace versus War Operations...incorporated into normal operating procedures. Distribution ManaQement. Distribution management was plagued with confusion throughout DS\\DS. This...to carrier terminals, depots and vendors. TDS recommendations to address the distribution management issue focused on: 1. Authorization of direct

Simulating Univariate and Multivariate Burr Type IIII and Type XII Distributions through the Method of L-Moments

ERIC Educational Resources Information Center

Pant, Mohan Dev

2011-01-01

The Burr families (Type III and Type XII) of distributions are traditionally used in the context of statistical modeling and for simulating non-normal distributions with moment-based parameters (e.g., Skew and Kurtosis). In educational and psychological studies, the Burr families of distributions can be used to simulate extremely asymmetrical and…

Money-center structures in dynamic banking systems

NASA Astrophysics Data System (ADS)

Li, Shouwei; Zhang, Minghui

2016-10-01

In this paper, we propose a dynamic model for banking systems based on the description of balance sheets. It generates some features identified through empirical analysis. Through simulation analysis of the model, we find that banking systems have the feature of money-center structures, that bank asset distributions are power-law distributions, and that contract size distributions are log-normal distributions.

Best Statistical Distribution of flood variables for Johor River in Malaysia

NASA Astrophysics Data System (ADS)

Salarpour Goodarzi, M.; Yusop, Z.; Yusof, F.

2012-12-01

A complex flood event is always characterized by a few characteristics such as flood peak, flood volume, and flood duration, which might be mutually correlated. This study explored the statistical distribution of peakflow, flood duration and flood volume at Rantau Panjang gauging station on the Johor River in Malaysia. Hourly data were recorded for 45 years. The data were analysed based on water year (July - June). Five distributions namely, Log Normal, Generalize Pareto, Log Pearson, Normal and Generalize Extreme Value (GEV) were used to model the distribution of all the three variables. Anderson-Darling and Kolmogorov-Smirnov goodness-of-fit tests were used to evaluate the best fit. Goodness-of-fit tests at 5% level of significance indicate that all the models can be used to model the distribution of peakflow, flood duration and flood volume. However, Generalize Pareto distribution is found to be the most suitable model when tested with the Anderson-Darling test and the, Kolmogorov-Smirnov suggested that GEV is the best for peakflow. The result of this research can be used to improve flood frequency analysis. Comparison between Generalized Extreme Value, Generalized Pareto and Log Pearson distributions in the Cumulative Distribution Function of peakflow

Charting the Course for Civil Affairs in the New Normal

DTIC Science & Technology

2015-07-01

Select a caveat Unlimited distribution Charting the Course for Civil Affairs in the New Normal Vera Zakem and Emily Mushen July...11  Challenges for Joint CA in the New Normal Environment ............................................ 13  New requirements for ...deliver essential services in preparation for handing full control back to the host nation government. Other independent civil affairs teams worked

Not Quite Normal: Consequences of Violating the Assumption of Normality in Regression Mixture Models

ERIC Educational Resources Information Center

Van Horn, M. Lee; Smith, Jessalyn; Fagan, Abigail A.; Jaki, Thomas; Feaster, Daniel J.; Masyn, Katherine; Hawkins, J. David; Howe, George

2012-01-01

Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of…

Simulation techniques for estimating error in the classification of normal patterns

NASA Technical Reports Server (NTRS)

Whitsitt, S. J.; Landgrebe, D. A.

1974-01-01

Methods of efficiently generating and classifying samples with specified multivariate normal distributions were discussed. Conservative confidence tables for sample sizes are given for selective sampling. Simulation results are compared with classified training data. Techniques for comparing error and separability measure for two normal patterns are investigated and used to display the relationship between the error and the Chernoff bound.

Normal probability plots with confidence.

PubMed

Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J; Wan, Fang

2015-01-01

Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Structural Features of the Western Taiwan Foreland Basin in the Eastern Taiwan Strait since Late Miocene

NASA Astrophysics Data System (ADS)

WANG, J. H.; Liu, C. S.; Chang, J. H.; Yang, E. Y.

2017-12-01

The western Taiwan Foreland Basin lies on the eastern part of Taiwan Strait. The structures in this region are dominated by crustal stretch and a series of flexural normal faults have been developed since Late Miocene owing to the flexural of Eurasia Plate. Through deciphering multi-channel seismic data and drilling data, these flexural features are observed in the offshore Changhua coastal area. The flexure normal faults are important features to realize structural activity in the western Taiwan Foreland Basin. Yang et al. (2016) mention that the reactivated normal faults are found north of the Zhushuixi estuary. It should be a significant issue to decipher whether these faults are still active. In this study, we have analyzed all the available seismic reflections profiles in the central part of the Taiwan Strait, and have observed many pre-Pliocene normal faults that are mainly distributed in the middle of the Taiwan Strait to Changyun Rise, and we tentatively suggest that the formation of these faults may be associated with the formation of the foreland basal unconformity. Furthermore, we will map the distribution of these normal faults and examine whether the reactivated normal faults have extended to south of the Zhushuixi estuary. Finally, we discuss the relation between the reactivated normal faults in the Taiwan Strait and those faults onshore. Key words: Multichannel seismic reflection profile, Taiwan Strait, Foreland basin, normal fault.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kelekis, Alexios, E-mail: akelekis@med.uoa.gr; Filippiadis, Dimitrios K., E-mail: dfilippiadis@yahoo.gr; Vergadis, Chrysovalantis, E-mail: valvergadis@yahoo.gr

PurposeThrough a prospective comparison of patients with vertebral fractures and normal population, we illustrate effect of percutaneous vertebroplasty (PV) upon projection of load distribution changes.MethodsVertebroplasty group (36 symptomatic patients with osteoporotic vertebral fractures) was evaluated on an electronic baropodometer registering projection of weight bearing areas on feet. Load distribution between right and left foot (including rear-front of the same foot) during standing and walking was recorded and compared before (group V1) and the day after (group V2) PV. Control group (30 healthy asymptomatic volunteers-no surgery record) were evaluated on the same baropodometer.ResultsMean value of load distribution difference between rear-front ofmore » the same foot was 9.45 ± 6.79 % (54.72–45.28 %) upon standing and 14.76 ± 7.09 % (57.38–42.62 %) upon walking in the control group. Respective load distribution values before PV were 16.52 ± 11.23 and 30.91 ± 19.26 % and after PV were 10.08 ± 6.26 and 14.25 ± 7.68 % upon standing and walking respectively. Mean value of load distribution variation between the two feet was 6.36 and 14.6 % before and 4.62 and 10.4 % after PV upon standing and walking respectively. Comparison of load distribution variation (group V1–V2, group V1-control group) is statistically significant. Comparison of load distribution variation (group V2-control group) is not statistically significant. Comparison of load distribution variation among the two feet is statistically significant during walking but not statistically significant during standing.ConclusionsThere is a statistically significant difference when comparing load distribution variation prior vertebroplasty and that of normal population. After vertebroplasty, this difference normalizes in a statistically significant way. PV is efficient on equilibrium-load distribution improvement as well.« less

Optimization of b-value distribution for biexponential diffusion-weighted MR imaging of normal prostate.

PubMed

Jambor, Ivan; Merisaari, Harri; Aronen, Hannu J; Järvinen, Jukka; Saunavaara, Jani; Kauko, Tommi; Borra, Ronald; Pesola, Marko

2014-05-01

To determine the optimal b-value distribution for biexponential diffusion-weighted imaging (DWI) of normal prostate using both a computer modeling approach and in vivo measurements. Optimal b-value distributions for the fit of three parameters (fast diffusion Df, slow diffusion Ds, and fraction of fast diffusion f) were determined using Monte-Carlo simulations. The optimal b-value distribution was calculated using four individual optimization methods. Eight healthy volunteers underwent four repeated 3 Tesla prostate DWI scans using both 16 equally distributed b-values and an optimized b-value distribution obtained from the simulations. The b-value distributions were compared in terms of measurement reliability and repeatability using Shrout-Fleiss analysis. Using low noise levels, the optimal b-value distribution formed three separate clusters at low (0-400 s/mm2), mid-range (650-1200 s/mm2), and high b-values (1700-2000 s/mm2). Higher noise levels resulted into less pronounced clustering of b-values. The clustered optimized b-value distribution demonstrated better measurement reliability and repeatability in Shrout-Fleiss analysis compared with 16 equally distributed b-values. The optimal b-value distribution was found to be a clustered distribution with b-values concentrated in the low, mid, and high ranges and was shown to improve the estimation quality of biexponential DWI parameters of in vivo experiments. Copyright © 2013 Wiley Periodicals, Inc.

Thermal and log-normal distributions of plasma in laser driven Coulomb explosions of deuterium clusters

NASA Astrophysics Data System (ADS)

Barbarino, M.; Warrens, M.; Bonasera, A.; Lattuada, D.; Bang, W.; Quevedo, H. J.; Consoli, F.; de Angelis, R.; Andreoli, P.; Kimura, S.; Dyer, G.; Bernstein, A. C.; Hagel, K.; Barbui, M.; Schmidt, K.; Gaul, E.; Donovan, M. E.; Natowitz, J. B.; Ditmire, T.

2016-08-01

In this work, we explore the possibility that the motion of the deuterium ions emitted from Coulomb cluster explosions is highly disordered enough to resemble thermalization. We analyze the process of nuclear fusion reactions driven by laser-cluster interactions in experiments conducted at the Texas Petawatt laser facility using a mixture of D2+3He and CD4+3He cluster targets. When clusters explode by Coulomb repulsion, the emission of the energetic ions is “nearly” isotropic. In the framework of cluster Coulomb explosions, we analyze the energy distributions of the ions using a Maxwell-Boltzmann (MB) distribution, a shifted MB distribution (sMB), and the energy distribution derived from a log-normal (LN) size distribution of clusters. We show that the first two distributions reproduce well the experimentally measured ion energy distributions and the number of fusions from d-d and d-3He reactions. The LN distribution is a good representation of the ion kinetic energy distribution well up to high momenta where the noise becomes dominant, but overestimates both the neutron and the proton yields. If the parameters of the LN distributions are chosen to reproduce the fusion yields correctly, the experimentally measured high energy ion spectrum is not well represented. We conclude that the ion kinetic energy distribution is highly disordered and practically not distinguishable from a thermalized one.

Pan-European comparison of candidate distributions for climatological drought indices, SPI and SPEI

NASA Astrophysics Data System (ADS)

Stagge, James; Tallaksen, Lena; Gudmundsson, Lukas; Van Loon, Anne; Stahl, Kerstin

2013-04-01

Drought indices are vital to objectively quantify and compare drought severity, duration, and extent across regions with varied climatic and hydrologic regimes. The Standardized Precipitation Index (SPI), a well-reviewed meterological drought index recommended by the WMO, and its more recent water balance variant, the Standardized Precipitation-Evapotranspiration Index (SPEI) both rely on selection of univariate probability distributions to normalize the index, allowing for comparisons across climates. The SPI, considered a universal meteorological drought index, measures anomalies in precipitation, whereas the SPEI measures anomalies in climatic water balance (precipitation minus potential evapotranspiration), a more comprehensive measure of water availability that incorporates temperature. Many reviewers recommend use of the gamma (Pearson Type III) distribution for SPI normalization, while developers of the SPEI recommend use of the three parameter log-logistic distribution, based on point observation validation. Before the SPEI can be implemented at the pan-European scale, it is necessary to further validate the index using a range of candidate distributions to determine sensitivity to distribution selection, identify recommended distributions, and highlight those instances where a given distribution may not be valid. This study rigorously compares a suite of candidate probability distributions using WATCH Forcing Data, a global, historical (1958-2001) climate dataset based on ERA40 reanalysis with 0.5 x 0.5 degree resolution and bias-correction based on CRU-TS2.1 observations. Using maximum likelihood estimation, alternative candidate distributions are fit for the SPI and SPEI across the range of European climate zones. When evaluated at this scale, the gamma distribution for the SPI results in negatively skewed values, exaggerating the index severity of extreme dry conditions, while decreasing the index severity of extreme high precipitation. This bias is particularly notable for shorter aggregation periods (1-6 months) during the summer months in southern Europe (below 45° latitude), and can partially be attributed to distribution fitting difficulties in semi-arid regions where monthly precipitation totals cluster near zero. By contrast, the SPEI has potential for avoiding this fitting difficulty because it is not bounded by zero. However, the recommended log-logistic distribution produces index values with less variation than the standard normal distribution. Among the alternative candidate distributions, the best fit distribution and the distribution parameters vary in space and time, suggesting regional commonalities within hydroclimatic regimes, as discussed further in the presentation.

Distribution of Auditory Response Behaviors in Normal Infants and Profoundly Multihandicapped Children.

ERIC Educational Resources Information Center

Flexer, Carol; Gans, Donald P.

1986-01-01

A study compared the responsiveness to sound by normal infants and profoundly multihandicapped children. Results revealed that the profoundly multihandicapped subjects displayed relatively more reflexive than attentive type behaviors and exhibited fewer behaviors per response. (Author/CB)

Scale Mixture Models with Applications to Bayesian Inference

NASA Astrophysics Data System (ADS)

Qin, Zhaohui S.; Damien, Paul; Walker, Stephen

2003-11-01

Scale mixtures of uniform distributions are used to model non-normal data in time series and econometrics in a Bayesian framework. Heteroscedastic and skewed data models are also tackled using scale mixture of uniform distributions.

Imaging surface contacts: Power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic

USGS Publications Warehouse

Dieterich, J.H.; Kilgore, B.D.

1996-01-01

A procedure has been developed to obtain microscope images of regions of contact between roughened surfaces of transparent materials, while the surfaces are subjected to static loads or undergoing frictional slip. Static loading experiments with quartz, calcite, soda-lime glass and acrylic plastic at normal stresses to 30 MPa yield power law distributions of contact areas from the smallest contacts that can be resolved (3.5 ??m2) up to a limiting size that correlates with the grain size of the abrasive grit used to roughen the surfaces. In each material, increasing normal stress results in a roughly linear increase of the real area of contact. Mechanisms of contact area increase are by growth of existing contacts, coalescence of contacts and appearance of new contacts. Mean contacts stresses are consistent with the indentation strength of each material. Contact size distributions are insensitive to normal stress indicating that the increase of contact area is approximately self-similar. The contact images and contact distributions are modeled using simulations of surfaces with random fractal topographies. The contact process for model fractal surfaces is represented by the simple expedient of removing material at regions where surface irregularities overlap. Synthetic contact images created by this approach reproduce observed characteristics of the contacts and demonstrate that the exponent in the power law distributions depends on the scaling exponent used to generate the surface topography.

Optical clock distribution in supercomputers using polyimide-based waveguides

NASA Astrophysics Data System (ADS)

Bihari, Bipin; Gan, Jianhua; Wu, Linghui; Liu, Yujie; Tang, Suning; Chen, Ray T.

1999-04-01

Guided-wave optics is a promising way to deliver high-speed clock-signal in supercomputer with minimized clock-skew. Si- CMOS compatible polymer-based waveguides for optoelectronic interconnects and packaging have been fabricated and characterized. A 1-to-48 fanout optoelectronic interconnection layer (OIL) structure based on Ultradel 9120/9020 for the high-speed massive clock signal distribution for a Cray T-90 supercomputer board has been constructed. The OIL employs multimode polymeric channel waveguides in conjunction with surface-normal waveguide output coupler and 1-to-2 splitters. Surface-normal couplers can couple the optical clock signals into and out from the H-tree polyimide waveguides surface-normally, which facilitates the integration of photodetectors to convert optical-signal to electrical-signal. A 45-degree surface- normal couplers has been integrated at each output end. The measured output coupling efficiency is nearly 100 percent. The output profile from 45-degree surface-normal coupler were calculated using Fresnel approximation. the theoretical result is in good agreement with experimental result. A total insertion loss of 7.98 dB at 850 nm was measured experimentally.

Comparison of low-altitude wind-shear statistics derived from measured and proposed standard wind profiles

NASA Technical Reports Server (NTRS)

Usry, J. W.

1983-01-01

Wind shear statistics were calculated for a simulated set of wind profiles based on a proposed standard wind field data base. Wind shears were grouped in altitude in altitude bands of 100 ft between 100 and 1400 ft and in wind shear increments of 0.025 knot/ft. Frequency distributions, means, and standard deviations for each altitude band were derived for the total sample were derived for both sets. It was found that frequency distributions in each altitude band for the simulated data set were more dispersed below 800 ft and less dispersed above 900 ft than those for the measured data set. Total sample frequency of occurrence for the two data sets was about equal for wind shear values between +0.075 knot/ft, but the simulated data set had significantly larger values for all wind shears outside these boundaries. It is shown that normal distribution in both data sets neither data set was normally distributed; similar results are observed from the cumulative frequency distributions.

Inverse estimation of the spheroidal particle size distribution using Ant Colony Optimization algorithms in multispectral extinction technique

NASA Astrophysics Data System (ADS)

He, Zhenzong; Qi, Hong; Wang, Yuqing; Ruan, Liming

2014-10-01

Four improved Ant Colony Optimization (ACO) algorithms, i.e. the probability density function based ACO (PDF-ACO) algorithm, the Region ACO (RACO) algorithm, Stochastic ACO (SACO) algorithm and Homogeneous ACO (HACO) algorithm, are employed to estimate the particle size distribution (PSD) of the spheroidal particles. The direct problems are solved by the extended Anomalous Diffraction Approximation (ADA) and the Lambert-Beer law. Three commonly used monomodal distribution functions i.e. the Rosin-Rammer (R-R) distribution function, the normal (N-N) distribution function, and the logarithmic normal (L-N) distribution function are estimated under dependent model. The influence of random measurement errors on the inverse results is also investigated. All the results reveal that the PDF-ACO algorithm is more accurate than the other three ACO algorithms and can be used as an effective technique to investigate the PSD of the spheroidal particles. Furthermore, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution functions to retrieve the PSD of spheroidal particles using PDF-ACO algorithm. The investigation shows a reasonable agreement between the original distribution function and the general distribution function when only considering the variety of the length of the rotational semi-axis.

Growth models and the expected distribution of fluctuating asymmetry

USGS Publications Warehouse

Graham, John H.; Shimizu, Kunio; Emlen, John M.; Freeman, D. Carl; Merkel, John

2003-01-01

Multiplicative error accounts for much of the size-scaling and leptokurtosis in fluctuating asymmetry. It arises when growth involves the addition of tissue to that which is already present. Such errors are lognormally distributed. The distribution of the difference between two lognormal variates is leptokurtic. If those two variates are correlated, then the asymmetry variance will scale with size. Inert tissues typically exhibit additive error and have a gamma distribution. Although their asymmetry variance does not exhibit size-scaling, the distribution of the difference between two gamma variates is nevertheless leptokurtic. Measurement error is also additive, but has a normal distribution. Thus, the measurement of fluctuating asymmetry may involve the mixing of additive and multiplicative error. When errors are multiplicative, we recommend computing log E(l) − log E(r), the difference between the logarithms of the expected values of left and right sides, even when size-scaling is not obvious. If l and r are lognormally distributed, and measurement error is nil, the resulting distribution will be normal, and multiplicative error will not confound size-related changes in asymmetry. When errors are additive, such a transformation to remove size-scaling is unnecessary. Nevertheless, the distribution of l − r may still be leptokurtic.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

NASA Astrophysics Data System (ADS)

Yan, Qiushuang; Zhang, Jie; Fan, Chenqing; Wang, Jing; Meng, Junmin

2018-01-01

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram-Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram-Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram-Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

a Heuristic Approach for Multi Objective Distribution Feeder Reconfiguration: Using Fuzzy Sets in Normalization of Objective Functions

NASA Astrophysics Data System (ADS)

Milani, Armin Ebrahimi; Haghifam, Mahmood Reza

2008-10-01

The reconfiguration is an operation process used for optimization with specific objectives by means of changing the status of switches in a distribution network. In this paper each objectives is normalized with inspiration from fuzzy sets-to cause optimization more flexible- and formulized as a unique multi-objective function. The genetic algorithm is used for solving the suggested model, in which there is no risk of non-liner objective functions and constraints. The effectiveness of the proposed method is demonstrated through the examples.

29 CFR 4041.22 - Administration of plan during pendency of termination process.

Code of Federal Regulations, 2010 CFR

2010-07-01

... out the normal operations of the plan. During that time period, except as provided in paragraph (b) of... Code to receive the distribution; (2) The distribution is consistent with prior plan practice; and (3) The distribution is not reasonably expected to jeopardize the plan's sufficiency for plan benefits. ...

Detection of Person Misfit in Computerized Adaptive Tests with Polytomous Items.

ERIC Educational Resources Information Center

van Krimpen-Stoop, Edith M. L. A.; Meijer, Rob R.

2002-01-01

Compared the nominal and empirical null distributions of the standardized log-likelihood statistic for polytomous items for paper-and-pencil (P&P) and computerized adaptive tests (CATs). Results show that the empirical distribution of the statistic differed from the assumed standard normal distribution for both P&P tests and CATs. Also…

Distribution of water quality parameters in Dhemaji district, Assam (India).

PubMed

Buragohain, Mridul; Bhuyan, Bhabajit; Sarma, H P

2010-07-01

The primary objective of this study is to present a statistically significant water quality database of Dhemaji district, Assam (India) with special reference to pH, fluoride, nitrate, arsenic, iron, sodium and potassium. 25 water samples collected from different locations of five development blocks in Dhemaji district have been studied separately. The implications presented are based on statistical analyses of the raw data. Normal distribution statistics and reliability analysis (correlation and covariance matrix) have been employed to find out the distribution pattern, localisation of data, and other related information. Statistical observations show that all the parameters under investigation exhibit non uniform distribution with a long asymmetric tail either on the right or left side of the median. The width of the third quartile was consistently found to be more than the second quartile for each parameter. Differences among mean, mode and median, significant skewness and kurtosis value indicate that the distribution of various water quality parameters in the study area is widely off normal. Thus, the intrinsic water quality is not encouraging due to unsymmetrical distribution of various water quality parameters in the study area.

Simulation of real-gas effects on pressure distributions for aeroassist flight experiment vehicle and comparison with prediction

NASA Technical Reports Server (NTRS)

Micol, John R.

1992-01-01

Pressure distributions measured on a 60 degree half-angle elliptic cone, raked off at an angle of 73 degrees from the cone centerline and having an ellipsoid nose (ellipticity equal to 2.0 in the symmetry plane) are presented for angles of attack from -10 degrees to 10 degrees. The high normal shock density ratio aspect of a real gas was simulated by testing in Mach 6 air and CF sub 4 (density ratio equal to 5.25 and 12.0, respectively). The effects of Reynolds number, angle of attack, and normal shock density ratio on these measurements are examined, and comparisons with a three dimensional Euler code known as HALIS are made. A significant effect of density ratio on pressure distributions on the cone section of the configuration was observed; the magnitude of this effect decreased with increasing angle of attack. The effect of Reynolds number on pressure distributions was negligible for forebody pressure distributions, but a measurable effect was noted on base pressures. In general, the HALIS code accurately predicted the measured pressure distributions in air and CF sub 4.

Individual vision and peak distribution in collective actions

NASA Astrophysics Data System (ADS)

Lu, Peng

2017-06-01

People make decisions on whether they should participate as participants or not as free riders in collective actions with heterogeneous visions. Besides of the utility heterogeneity and cost heterogeneity, this work includes and investigates the effect of vision heterogeneity by constructing a decision model, i.e. the revised peak model of participants. In this model, potential participants make decisions under the joint influence of utility, cost, and vision heterogeneities. The outcomes of simulations indicate that vision heterogeneity reduces the values of peaks, and the relative variance of peaks is stable. Under normal distributions of vision heterogeneity and other factors, the peaks of participants are normally distributed as well. Therefore, it is necessary to predict distribution traits of peaks based on distribution traits of related factors such as vision heterogeneity and so on. We predict the distribution of peaks with parameters of both mean and standard deviation, which provides the confident intervals and robust predictions of peaks. Besides, we validate the peak model of via the Yuyuan Incident, a real case in China (2014), and the model works well in explaining the dynamics and predicting the peak of real case.

CDC6600 subroutine for normal random variables. [RVNORM (RMU, SIG)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amos, D.E.

1977-04-01

A value y for a uniform variable on (0,1) is generated and a table of 96-percent points for the (0,1) normal distribution is interpolated for a value of the normal variable x(0,1) on 0.02 less than or equal to y less than or equal to 0.98. For the tails, the inverse normal is computed by a rational Chebyshev approximation in an appropriate variable. Then X = x sigma + ..mu.. gives the X(..mu..,sigma) variable.

Multiplicative Modeling of Children's Growth and Its Statistical Properties

NASA Astrophysics Data System (ADS)

Kuninaka, Hiroto; Matsushita, Mitsugu

2014-03-01

We develop a numerical growth model that can predict the statistical properties of the height distribution of Japanese children. Our previous studies have clarified that the height distribution of schoolchildren shows a transition from the lognormal distribution to the normal distribution during puberty. In this study, we demonstrate by simulation that the transition occurs owing to the variability of the onset of puberty.

A note on `Analysis of gamma-ray burst duration distribution using mixtures of skewed distributions'

NASA Astrophysics Data System (ADS)

Kwong, Hok Shing; Nadarajah, Saralees

2018-01-01

Tarnopolski [Monthly Notices of the Royal Astronomical Society, 458 (2016) 2024-2031] analysed data sets on gamma-ray burst durations using skew distributions. He showed that the best fits are provided by two skew normal and three Gaussian distributions. Here, we suggest other distributions, including some that are heavy tailed. At least one of these distributions is shown to provide better fits than those considered in Tarnopolski. Five criteria are used to assess best fits.

Distribution of intravenously administered acetylcholinesterase inhibitor and acetylcholinesterase activity in the adrenal gland: 11C-donepezil PET study in the normal rat.

PubMed

Watabe, Tadashi; Naka, Sadahiro; Ikeda, Hayato; Horitsugi, Genki; Kanai, Yasukazu; Isohashi, Kayako; Ishibashi, Mana; Kato, Hiroki; Shimosegawa, Eku; Watabe, Hiroshi; Hatazawa, Jun

2014-01-01

Acetylcholinesterase (AChE) inhibitors have been used for patients with Alzheimer's disease. However, its pharmacokinetics in non-target organs other than the brain has not been clarified yet. The purpose of this study was to evaluate the relationship between the whole-body distribution of intravenously administered (11)C-Donepezil (DNP) and the AChE activity in the normal rat, with special focus on the adrenal glands. The distribution of (11)C-DNP was investigated by PET/CT in 6 normal male Wistar rats (8 weeks old, body weight  = 220 ± 8.9 g). A 30-min dynamic scan was started simultaneously with an intravenous bolus injection of (11)C-DNP (45.0 ± 10.7 MBq). The whole-body distribution of the (11)C-DNP PET was evaluated based on the Vt (total distribution volume) by Logan-plot analysis. A fluorometric assay was performed to quantify the AChE activity in homogenized tissue solutions of the major organs. The PET analysis using Vt showed that the adrenal glands had the 2nd highest level of (11)C-DNP in the body (following the liver) (13.33 ± 1.08 and 19.43 ± 1.29 ml/cm(3), respectively), indicating that the distribution of (11)C-DNP was the highest in the adrenal glands, except for that in the excretory organs. The AChE activity was the third highest in the adrenal glands (following the small intestine and the stomach) (24.9 ± 1.6, 83.1 ± 3.0, and 38.5 ± 8.1 mU/mg, respectively), indicating high activity of AChE in the adrenal glands. We demonstrated the whole-body distribution of (11)C-DNP by PET and the AChE activity in the major organs by fluorometric assay in the normal rat. High accumulation of (11)C-DNP was observed in the adrenal glands, which suggested the risk of enhanced cholinergic synaptic transmission by the use of AChE inhibitors.

Surface normal velocity distribution of sputtered Zr-atoms for light-ion irradiation

NASA Astrophysics Data System (ADS)

Bay, H. L.; Berres, W.; Hintz, E.

1982-03-01

The velocity distribution of sputtered Zr-atoms has been measured for 8 keV Ar + and He + ions and 2.5 keV D + ion irradiation at normal incidence. The measurements were performed with the aid of laser induced fluorescence spectroscopy (LIFS) using a CW-laser pumped dye-laser. The influence of the measuring geometry was investigated and found to be in good agreement with calculation. For light-ion sputtering the collision-cascade theory is no longer applicable. Here a distinct shift in the velocity distributions towards lower velocities compared with the Ar results was found. The shift can be correlated to anisotropic effects in connection with the change in the maximum recoil energy Tm in the cascade.

Statistical distribution of mechanical properties for three graphite-epoxy material systems

NASA Technical Reports Server (NTRS)

Reese, C.; Sorem, J., Jr.

1981-01-01

Graphite-epoxy composites are playing an increasing role as viable alternative materials in structural applications necessitating thorough investigation into the predictability and reproducibility of their material strength properties. This investigation was concerned with tension, compression, and short beam shear coupon testing of large samples from three different material suppliers to determine their statistical strength behavior. Statistical results indicate that a two Parameter Weibull distribution model provides better overall characterization of material behavior for the graphite-epoxy systems tested than does the standard Normal distribution model that is employed for most design work. While either a Weibull or Normal distribution model provides adequate predictions for average strength values, the Weibull model provides better characterization in the lower tail region where the predictions are of maximum design interest. The two sets of the same material were found to have essentially the same material properties, and indicate that repeatability can be achieved.

Empirical study of the tails of mutual fund size

NASA Astrophysics Data System (ADS)

Schwarzkopf, Yonathan; Farmer, J. Doyne

2010-06-01

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distribution. We study the distribution empirically and show that the tail is much better described by a log-normal than a power law, indicating less concentration than, for example, personal income. The results are highly statistically significant and are consistent across fifteen years. This contradicts a recent theory concerning the origin of the power law tails of the trading volume distribution. Based on the analysis in a companion paper, the log-normality is to be expected, and indicates that the distribution of mutual funds remains perpetually out of equilibrium.

Probabilistic model of bridge vehicle loads in port area based on in-situ load testing

NASA Astrophysics Data System (ADS)

Deng, Ming; Wang, Lei; Zhang, Jianren; Wang, Rei; Yan, Yanhong

2017-11-01

Vehicle load is an important factor affecting the safety and usability of bridges. An statistical analysis is carried out in this paper to investigate the vehicle load data of Tianjin Haibin highway in Tianjin port of China, which are collected by the Weigh-in- Motion (WIM) system. Following this, the effect of the vehicle load on test bridge is calculated, and then compared with the calculation result according to HL-93(AASHTO LRFD). Results show that the overall vehicle load follows a distribution with a weighted sum of four normal distributions. The maximum vehicle load during the design reference period follows a type I extremum distribution. The vehicle load effect also follows a weighted sum of four normal distributions, and the standard value of the vehicle load is recommended as 1.8 times that of the calculated value according to HL-93.

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

Holland, M.D.; Gray, B.R.

2011-01-01

Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.

Direct comparison between the angular distributions of the erythemal and eye-damaging UV irradiances: a pilot study.

PubMed

Schouten, P; Parisi, A V

2011-02-07

Several broadband ultraviolet (UV) radiation angular distribution investigations have been previously presented. As the biologically damaging effectiveness of UV radiation is known to be wavelength dependent, it is necessary to expand this research into the distribution of the spectral UV. UV radiation is also susceptible to Rayleigh and Mie scattering processes, both of which are completely wavelength dependent. Additionally, the majority of previous measurements detailing the biologically damaging effect of spectral UV radiation have been oriented with respect to the horizontal plane or in a plane directed towards the sun (sun-normal), with the irradiance weighted against action spectra formulated specifically for human skin and tissue. However, the human body consists of very few horizontal or sun-normal surfaces. Extending the previous research by measuring the distribution of the spectral irradiance across the sky for the complete terrestrial solar UV waveband and weighting it against erythemal, photoconjunctivital and photokeratital action spectra allowed for the analysis of the differences between the biologically effective irradiance (UV(BE)) values intercepted at different orientations and the effect of scattering processes upon the homogeneity of these UV(BE) distributions. It was established that under the local atmospheric environment, the distribution profile of the UV(BE) for each biological response was anisotropic, with the highest intensities generally intercepted at inclination angles situated between the horizontal and vertical planes along orientations closely coinciding with the sun-normal. A finding from this was that the angular distributions of the erythemal UV(BE) and the photoconjunctivital UV(BE) were different, due to the differential scattering between the shorter and longer UV wavelengths within the atmosphere. Copyright © 2010 Elsevier B.V. All rights reserved.

Thermal modelling of normal distributed nanoparticles through thickness in an inorganic material matrix

NASA Astrophysics Data System (ADS)

Latré, S.; Desplentere, F.; De Pooter, S.; Seveno, D.

2017-10-01

Nanoscale materials showing superior thermal properties have raised the interest of the building industry. By adding these materials to conventional construction materials, it is possible to decrease the total thermal conductivity by almost one order of magnitude. This conductivity is mainly influenced by the dispersion quality within the matrix material. At the industrial scale, the main challenge is to control this dispersion to reduce or even eliminate thermal bridges. This allows to reach an industrially relevant process to balance out the high material cost and their superior thermal insulation properties. Therefore, a methodology is required to measure and describe these nanoscale distributions within the inorganic matrix material. These distributions are either random or normally distributed through thickness within the matrix material. We show that the influence of these distributions is meaningful and modifies the thermal conductivity of the building material. Hence, this strategy will generate a thermal model allowing to predict the thermal behavior of the nanoscale particles and their distributions. This thermal model will be validated by the hot wire technique. For the moment, a good correlation is found between the numerical results and experimental data for a randomly distributed form of nanoparticles in all directions.

Is It Time to Change Our Reference Curve for Femur Length? Using the Z-Score to Select the Best Chart in a Chinese Population

PubMed Central

Yang, Huixia; Wei, Yumei; Su, Rina; Wang, Chen; Meng, Wenying; Wang, Yongqing; Shang, Lixin; Cai, Zhenyu; Ji, Liping; Wang, Yunfeng; Sun, Ying; Liu, Jiaxiu; Wei, Li; Sun, Yufeng; Zhang, Xueying; Luo, Tianxia; Chen, Haixia; Yu, Lijun

2016-01-01

Objective To use Z-scores to compare different charts of femur length (FL) applied to our population with the aim of identifying the most appropriate chart. Methods A retrospective study was conducted in Beijing. Fifteen hospitals in Beijing were chosen as clusters using a systemic cluster sampling method, in which 15,194 pregnant women delivered from June 20th to November 30th, 2013. The measurements of FL in the second and third trimester were recorded, as well as the last measurement obtained before delivery. Based on the inclusion and exclusion criteria, we identified FL measurements from 19996 ultrasounds from 7194 patients between 11 and 42 weeks gestation. The FL data were then transformed into Z-scores that were calculated using three series of reference equations obtained from three reports: Leung TN, Pang MW et al (2008); Chitty LS, Altman DG et al (1994); and Papageorghiou AT et al (2014). Each Z-score distribution was presented as the mean and standard deviation (SD). Skewness and kurtosis and were compared with the standard normal distribution using the Kolmogorov-Smirnov test. The histogram of their distributions was superimposed on the non-skewed standard normal curve (mean = 0, SD = 1) to provide a direct visual impression. Finally, the sensitivity and specificity of each reference chart for identifying fetuses <5th or >95th percentile (based on the observed distribution of Z-scores) were calculated. The Youden index was also listed. A scatter diagram with the 5th, 50th, and 95th percentile curves calculated from and superimposed on each reference chart was presented to provide a visual impression. Results The three Z-score distribution curves appeared to be normal, but none of them matched the expected standard normal distribution. In our study, the Papageorghiou reference curve provided the best results, with a sensitivity of 100% for identifying fetuses with measurements < 5th and > 95th percentile, and specificities of 99.9% and 81.5%, respectively. Conclusions It is important to choose an appropriate reference curve when defining what is normal. The Papageorghiou reference curve for FL seems to be the best fit for our population. Perhaps it is time to change our reference curve for femur length. PMID:27458922

Distribution of normal superficial ocular vessels in digital images.

PubMed

Banaee, Touka; Ehsaei, Asieh; Pourreza, Hamidreza; Khajedaluee, Mohammad; Abrishami, Mojtaba; Basiri, Mohsen; Daneshvar Kakhki, Ramin; Pourreza, Reza

2014-02-01

To investigate the distribution of different-sized vessels in the digital images of the ocular surface, an endeavor which may provide useful information for future studies. This study included 295 healthy individuals. From each participant, four digital photographs of the superior and inferior conjunctivae of both eyes, with a fixed succession of photography (right upper, right lower, left upper, left lower), were taken with a slit lamp mounted camera. Photographs were then analyzed by a previously described algorithm for vessel detection in the digital images. The area (of the image) occupied by vessels (AOV) of different sizes was measured. Height, weight, fasting blood sugar (FBS) and hemoglobin levels were also measured and the relationship between these parameters and the AOV was investigated. These findings indicated a statistically significant difference in the distribution of the AOV among the four conjunctival areas. No significant correlations were noted between the AOV of each conjunctival area and the different demographic and biometric factors. Medium-sized vessels were the most abundant vessels in the photographs of the four investigated conjunctival areas. The AOV of the different sizes of vessels follows a normal distribution curve in the four areas of the conjunctiva. The distribution of the vessels in successive photographs changes in a specific manner, with the mean AOV becoming larger as the photos were taken from the right upper to the left lower area. The AOV of vessel sizes has a normal distribution curve and medium-sized vessels occupy the largest area of the photograph. Copyright © 2013 British Contact Lens Association. Published by Elsevier Ltd. All rights reserved.

Distribution Development for STORM Ingestion Input Parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fulton, John

The Sandia-developed Transport of Radioactive Materials (STORM) code suite is used as part of the Radioisotope Power System Launch Safety (RPSLS) program to perform statistical modeling of the consequences due to release of radioactive material given a launch accident. As part of this modeling, STORM samples input parameters from probability distributions with some parameters treated as constants. This report described the work done to convert four of these constant inputs (Consumption Rate, Average Crop Yield, Cropland to Landuse Database Ratio, and Crop Uptake Factor) to sampled values. Consumption rate changed from a constant value of 557.68 kg / yr tomore » a normal distribution with a mean of 102.96 kg / yr and a standard deviation of 2.65 kg / yr. Meanwhile, Average Crop Yield changed from a constant value of 3.783 kg edible / m 2 to a normal distribution with a mean of 3.23 kg edible / m 2 and a standard deviation of 0.442 kg edible / m 2 . The Cropland to Landuse Database ratio changed from a constant value of 0.0996 (9.96%) to a normal distribution with a mean value of 0.0312 (3.12%) and a standard deviation of 0.00292 (0.29%). Finally the crop uptake factor changed from a constant value of 6.37e -4 (Bq crop /kg)/(Bq soil /kg) to a lognormal distribution with a geometric mean value of 3.38e -4 (Bq crop /kg)/(Bq soil /kg) and a standard deviation value of 3.33 (Bq crop /kg)/(Bq soil /kg)« less

14 CFR 23.321 - General.

Code of Federal Regulations, 2010 CFR

2010-01-01

... STANDARDS: NORMAL, UTILITY, ACROBATIC, AND COMMUTER CATEGORY AIRPLANES Structure Flight Loads § 23.321 General. (a) Flight load factors represent the ratio of the aerodynamic force component (acting normal to... distribution of disposable load within the operating limitations specified in §§ 23.1583 through 23.1589. (c...

Optical and Nanoparticle Analysis of Normal and Cancer Cells by Light Transmission Spectroscopy

NASA Astrophysics Data System (ADS)

Deatsch, Alison; Sun, Nan; Johnson, Jeffery; Stack, Sharon; Szajko, John; Sander, Christopher; Rebuyon, Roland; Easton, Judah; Tanner, Carol; Ruggiero, Steven

2015-03-01

We have investigated the optical properties of human oral and ovarian cancer and normal cells. Specifically, we have measured the absolute optical extinction for intra-cellular material (lysates) in aqueous suspension. Measurements were conducted over a wavelength range of 250 to 1000 nm with 1 nm resolution using Light Transmission Spectroscopy (LTS). This provides both the absolute extinction of materials under study and, with Mie inversion, the absolute number of particles of a given diameter as a function of diameter in the range of 1 to 3000 nm. Our preliminary studies show significant differences in both the extinction and particle size distributions associated with cancer versus normal cells, which appear to be correlated with differences in the particle size distribution in the range of approximately 50 to 250 nm. Especially significant is a clearly higher density of particles at about 100 nm and smaller for normal cells. Department of Physics, Harper Cancer Research Institute, and the Office of Research at the University of Notre Dame.

[Distribution of acetylator phenotypes in the normal Moscow city population and in chronic alcoholism].

PubMed

Lil'in, E T; Korsunskaia, M P; Meksin, V A; Drozdov, E S; Nazarov, V V

1984-09-01

The distribution of acetylator phenotypes was studied in 169 normal individuals of Moscow Russian population and 75 inhabitants of Moscow suffering from chronic alcoholism. Polymorphism was found by means of acetylation in both groups studied. The proportion of repeatability of rapid and slow acetylators amounts to 48 and 52% among normal individuals, 44 and 56% among those who suffer from chronic alcoholism. The comparative analyses of such repeatability within the classes resulted in authentic increase of the rate of rapid acetylators among the chronic alcoholics (chi 2 = 18.32; p less than 0.01); in comparison with normal individual groups, (the modes being in classes 50-60% and 80-90%, with the antimode 70-80%), a shift of one of the modes from the 50-60% class into the 60-70% class was traced among diseased individuals. It is supposed that chronic alcohol consumption stimulates the process of acetylation; possible reasons for this stimulation are discussed.

Vibrational spectral investigation on xanthine and its derivatives—theophylline, caffeine and theobromine

NASA Astrophysics Data System (ADS)

Gunasekaran, S.; Sankari, G.; Ponnusamy, S.

2005-01-01

A normal coordinate analysis has been carried out on four compounds having a similar ring structure with different side chain substitutions, which are xanthine, caffeine, theophylline, and theobromine. Xanthine is chemically known as 2,6-dihydroxy purine. Caffeine, theophylline and theobromine are methylated xanthines. Considering the methyl groups as point mass, the number of normal modes of vibrations can be distributed as Γ vib=27 A'+12 A″ based on C s point group symmetry associated with the structures. In the present work 15 A' and 12 A″ normal modes are considered. A new set of orthonormal symmetry co-ordinates have been constructed. Wilson's F- G matrix method has been adopted for the normal coordinate analysis. A satisfactory vibrational band assignment has been made by employing the FTIR and FT Raman spectra of the compounds. The potential energy distribution is calculated with the arrived values of the force constants and hence the agreement of the frequency assignment has been checked.

Occurrence and distribution of contaminants in bottom sediment and water of the Barron River Canal, Big Cypress National Preserve, Florida

USGS Publications Warehouse

Miller, Ronald L.; McPherson, Benjamin F.

2001-01-01

Trace elements and organic contaminants in bottom-sediment samples collected from 10 sites on the Barron River Canal and from one site on the Turner River in October 1998 had patterns of distribution that indicated different sources. At some sites on the Barron River Canal, lead, copper, and zinc, normalized to aluminum, exceeded limits normally considered as background and may be enriched by human activities. Polynuclear aromatic hydrocarbons and p-cresol, normalized against organic carbon, had patterns of distribution that indicated local sources of input from a road or vehicular traffic or from an old creosote wood treatment facility. Phthalate esters and the traces elements arsenic, cadmium, and zinc were more widely distributed with the highest normalized concentrations occurring at the Turner River background site, probably due to the high percentage of fine sediment (74% less than 63 micrometers) and high organic carbon concentration (42%) at that site and the binding effect of organic carbon on trace elements and trace organic compounds. Low concentrations of pesticides or pesticide degradation products were detected in bottom sediment (DDD and DDE, each less than 3.5 µg/kg) and water (9 pesticides, each less than 0.06 µ/L), primarily in the northern reach of the Barron River Canal where agriculture is a likely source. Although a few contaminants approached criteria that would indicate adverse effects on aquatic life, none exceeded the criteria, but the potential synergistic effects of mixtures of contaminants found at most sites are not included in the criteria.

Role of progenitor cell producing normal vagina by metaplasia in laparoscopic peritoneal vaginoplasty

PubMed Central

Mhatre, Pravin N.; Narkhede, Hemraj R.; Pawar, P. Amol; Mhatre, P. Jyoti; Kumar, Das Dhanjit

2016-01-01

CONTEXT: Host of vaginoplasty techniques have been described. None has been successful in developing normal vagina. Laparoscopic peritoneal vaginoplasty (LPV) is performed in Mayer–Rokitansky–Küster–Hauser syndrome (MRKHS) culminating in normal vagina. AIMS: This study aims to confirm normal development of neovagina by anatomical and functional parameters of histology, cytology, and ultrasonography (USG) in LPV. To identify peritoneal progenitor cell by OCT4/SOX2 markers. To demonstrate the metaplastic conversion of peritoneum to neovagina and the progenitor cell concentration, distribution pattern. SETTINGS AND DESIGN: This is prospective experimental study, conducted at teaching hospital and private hospital. SUBJECTS AND METHODS: Fifteen women of MRKHS underwent LPV followed by histology, cytology, two-/three-dimensional USG of neovagina. Four women underwent peritoneal biopsy for identification of progenitor cells with OCT4/SOX2 markers. One patient underwent serial biopsies for 4 weeks for histology and progenitor cell immunohistochemistry. RESULTS: Normal vaginal histology and cytology were apparent. USG of neovagina showed normal appearance and blood flow. Two peritoneal samples confirmed the presence of progenitor cells. Serial biopsies demonstrated the epithelial change from single to multilayer with stromal compaction and neoangiogenesis. The progenitor cells concentration and different distribution patterns were described using SOX2/OCT4 markers. CONCLUSIONS: We have shown successful peritoneal metaplastic conversion to normal vagina in LPV. The progenitor cell was identified in normal peritoneum using SOX2/OCT4 markers. The progenitor cell concentration and pattern were demonstrated at various stages of neovaginal development. PMID:28216908

Particle size distributions and gas-particle partitioning of polychlorinated dibenzo-p-dioxins and dibenzofurans in ambient air during haze days and normal days.

PubMed

Zhang, Xian; Zheng, Minghui; Liang, Yong; Liu, Guorui; Zhu, Qingqing; Gao, Lirong; Liu, Wenbin; Xiao, Ke; Sun, Xu

2016-12-15

Little information is available on the distributions of airborne polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) during haze days. In this study, PCDD/F concentrations, particle size distributions, and gas-particle partitioning in a Beijing suburban area during haze days and normal days were investigated. High PCDD/F concentrations, 3979-74,702fgm -3 (173-3885fgI-TEQm -3 ), were found during haze days and ~98% of the PCDD/Fs were associated with particles. Most PCDD/F congeners (>90%) were associated with particles. PCDD/F concentrations increased as particle sizes decreased and 95% of the particle-bound PCDD/Fs were associated with inhalable fine particles with aerodynamic diameters<2.5μm. PCDD/Fs were mainly absorbed in the particles and the Harner-Bidleman model predicted the particulate fractions of the PCDD/F congeners in the air samples well. The investigated PCDD/F concentrations and particle-bound distributions were different during normal days than during haze days. Temporal airborne PCDD/F trends in a suburban area during haze conditions could support better understanding of the exposure risk posed by toxic PCDD/Fs associated with fine particles. Copyright © 2016 Elsevier B.V. All rights reserved.

Distributive justice and cognitive enhancement in lower, normal intelligence.

PubMed

Dunlop, Mikael; Savulescu, Julian

2014-01-01

There exists a significant disparity within society between individuals in terms of intelligence. While intelligence varies naturally throughout society, the extent to which this impacts on the life opportunities it affords to each individual is greatly undervalued. Intelligence appears to have a prominent effect over a broad range of social and economic life outcomes. Many key determinants of well-being correlate highly with the results of IQ tests, and other measures of intelligence, and an IQ of 75 is generally accepted as the most important threshold in modern life. The ability to enhance our cognitive capacities offers an exciting opportunity to correct disabling natural variation and inequality in intelligence. Pharmaceutical cognitive enhancers, such as modafinil and methylphenidate, have been shown to have the capacity to enhance cognition in normal, healthy individuals. Perhaps of most relevance is the presence of an 'inverted U effect' for most pharmaceutical cognitive enhancers, whereby the degree of enhancement increases as intelligence levels deviate further below the mean. Although enhancement, including cognitive enhancement, has been much debated recently, we argue that there are egalitarian reasons to enhance individuals with low but normal intelligence. Under egalitarianism, cognitive enhancement has the potential to reduce opportunity inequality and contribute to relative income and welfare equality in the lower, normal intelligence subgroup. Cognitive enhancement use is justifiable under prioritarianism through various means of distribution; selective access to the lower, normal intelligence subgroup, universal access, or paradoxically through access primarily to the average and above average intelligence subgroups. Similarly, an aggregate increase in social well-being is achieved through similar means of distribution under utilitarianism. In addition, the use of cognitive enhancement within the lower, normal intelligence subgroup negates, or at the very least minimises, several common objections to cognitive enhancement. Subsequently, this paper demonstrates that there is a compelling case for cognitive enhancement use in individuals with lower, normal intelligence.

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

ERIC Educational Resources Information Center

Woods, Carol M.; Thissen, David

2006-01-01

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the…

Estimation of Item Parameters and the GEM Algorithm.

ERIC Educational Resources Information Center

Tsutakawa, Robert K.

The models and procedures discussed in this paper are related to those presented in Bock and Aitkin (1981), where they considered the 2-parameter probit model and approximated a normally distributed prior distribution of abilities by a finite and discrete distribution. One purpose of this paper is to clarify the nature of the general EM (GEM)…

Creating Composite Age Groups to Smooth Percentile Rank Distributions of Small Samples

ERIC Educational Resources Information Center

Lopez, Francesca; Olson, Amy; Bansal, Naveen

2011-01-01

Individually administered tests are often normed on small samples, a process that may result in irregularities within and across various age or grade distributions. Test users often smooth distributions guided by Thurstone assumptions (normality and linearity) to result in norms that adhere to assumptions made about how the data should look. Test…

Delineating generalized species boundaries from species distribution data and a species distribution model

Treesearch

Matthew P. Peters; Stephen N. Matthews; Louis R. Iverson; Anantha M. Prasad

2013-01-01

Species distribution models (SDM) are commonly used to provide information about species ranges or extents, and often are intended to represent the entire area of potential occupancy or suitable habitat in which individuals occur. While SDMs can provide results over various geographic extents, they normally operate within a grid and cannot delimit distinct, smooth...

Electron energy distribution in a helium plasma created by nuclear radiations

NASA Technical Reports Server (NTRS)

Lo, R. H.; Miley, G. H.

1974-01-01

An integral balance technique for calculation of the electron energy distribution in a radiation-induced plasma is described. Results predict W-values reasonably well and compare favorably with more complicated Monte-Carlo calculations. The distribution found differs from that in a normal electrical discharge and is of interest in radiation-pumped laser research.

Comparing Simulated and Theoretical Sampling Distributions of the U3 Person-Fit Statistic.

ERIC Educational Resources Information Center

Emons, Wilco H. M.; Meijer, Rob R.; Sijtsma, Klaas

2002-01-01

Studied whether the theoretical sampling distribution of the U3 person-fit statistic is in agreement with the simulated sampling distribution under different item response theory models and varying item and test characteristics. Simulation results suggest that the use of standard normal deviates for the standardized version of the U3 statistic may…

Normality of Residuals Is a Continuous Variable, and Does Seem to Influence the Trustworthiness of Confidence Intervals: A Response to, and Appreciation of, Williams, Grajales, and Kurkiewicz (2013)

ERIC Educational Resources Information Center

Osborne, Jason W.

2013-01-01

Osborne and Waters (2002) focused on checking some of the assumptions of multiple linear regression. In a critique of that paper, Williams, Grajales, and Kurkiewicz correctly clarify that regression models estimated using ordinary least squares require the assumption of normally distributed errors, but not the assumption of normally distributed…

A Computational Study of the Respiratory Airflow Characteristics in Normal and Obstructed Human Airways

DTIC Science & Technology

2014-01-01

normal and three different obstructed airway geometries, consisting of symmetric, asym- metric, and random obstructions. Fig. 2 shows the geometric ...normal and obstructed airways Airway resistance is a measure of the opposition to the airflow caused by geometric properties, such as airway obstruction...pressure drops. Resistance values were dependent on the degree and geometric distribution of the obstruction sites. In the symmetric obstruction model

Modeling extreme hurricane damage in the United States using generalized Pareto distribution

NASA Astrophysics Data System (ADS)

Dey, Asim Kumer

Extreme value distributions are used to understand and model natural calamities, man made catastrophes and financial collapses. Extreme value theory has been developed to study the frequency of such events and to construct a predictive model so that one can attempt to forecast the frequency of a disaster and the amount of damage from such a disaster. In this study, hurricane damages in the United States from 1900-2012 have been studied. The aim of the paper is three-fold. First, normalizing hurricane damage and fitting an appropriate model for the normalized damage data. Secondly, predicting the maximum economic damage from a hurricane in future by using the concept of return period. Finally, quantifying the uncertainty in the inference of extreme return levels of hurricane losses by using a simulated hurricane series, generated by bootstrap sampling. Normalized hurricane damage data are found to follow a generalized Pareto distribution. tion. It is demonstrated that standard deviation and coecient of variation increase with the return period which indicates an increase in uncertainty with model extrapolation.

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part I: Fundamentals

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2016-12-01

Recent advances in signal processing and structural dynamics have spurred the adoption of transmissibility functions in academia and industry alike. Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty impacts its applications. This study is focused on statistical inference for raw scalar transmissibility functions modeled as complex ratio random variables. The goal is achieved through companion papers. This paper (Part I) is dedicated to dealing with a formal mathematical proof. New theorems on multivariate circularly-symmetric complex normal ratio distribution are proved on the basis of principle of probabilistic transformation of continuous random vectors. The closed-form distributional formulas for multivariate ratios of correlated circularly-symmetric complex normal random variables are analytically derived. Afterwards, several properties are deduced as corollaries and lemmas to the new theorems. Monte Carlo simulation (MCS) is utilized to verify the accuracy of some representative cases. This work lays the mathematical groundwork to find probabilistic models for raw scalar transmissibility functions, which are to be expounded in detail in Part II of this study.

The effect of signal variability on the histograms of anthropomorphic channel outputs: factors resulting in non-normally distributed data

NASA Astrophysics Data System (ADS)

Elshahaby, Fatma E. A.; Ghaly, Michael; Jha, Abhinav K.; Frey, Eric C.

2015-03-01

Model Observers are widely used in medical imaging for the optimization and evaluation of instrumentation, acquisition parameters and image reconstruction and processing methods. The channelized Hotelling observer (CHO) is a commonly used model observer in nuclear medicine and has seen increasing use in other modalities. An anthropmorphic CHO consists of a set of channels that model some aspects of the human visual system and the Hotelling Observer, which is the optimal linear discriminant. The optimality of the CHO is based on the assumption that the channel outputs for data with and without the signal present have a multivariate normal distribution with equal class covariance matrices. The channel outputs result from the dot product of channel templates with input images and are thus the sum of a large number of random variables. The central limit theorem is thus often used to justify the assumption that the channel outputs are normally distributed. In this work, we aim to examine this assumption for realistically simulated nuclear medicine images when various types of signal variability are present.

XFM demonstrates preferential accumulation of a vanadyl-based MRI contrast agent in murine colonic tumors

PubMed Central

Mustafi, Devkumar; Ward, Jesse; Dougherty, Urszula; Bissonnette, Marc; Hart, John; Vogt, Stefan; Karczmar, Gregory S.

2016-01-01

Contrast agents that specifically enhance cancers on MRI would allow earlier detection. Vanadyl-based chelates (VCs) selectively enhance rodent cancers on MRI, suggesting selective uptake of VCs by cancers. Here we report X-ray fluorescence microscopy (XFM) of VC uptake by murine colon cancer. Colonic tumors in mice treated with azoxymethane/dextran sulfate sodium were identified by MRI. Then a gadolinium-based contrast agent and a VC were injected I.V.; mice were sacrificed and colons sectioned. VC distribution was sampled at 120 minutes after injection to evaluate the long term accumulation. Gadolinium distribution was sampled at 10 minutes after injection due to its rapid washout. XFM was performed on 72 regions of normal and cancerous colon from 5 normal mice and 4 cancer-bearing mice. XFM showed that all gadolinium was extracellular with similar concentrations in colon cancers and normal colon. In contrast, the average VC concentration was 2-fold higher in cancers vs. normal tissue (p<0.002). Cancers also contained numerous ‘hot spots’ with intracellular VC concentrations 6-fold higher than the concentration in normal colon (p<0.0001). No ‘hot spots’ were detected in normal colon. This is the first direct demonstration that VCs selectively accumulate in cancer cells, and thus may improve cancer detection. PMID:25813904

Obesity-Related Metabolic Risk in Sedentary Hispanic Adolescent Girls with Normal BMI.

PubMed

van der Heijden, Gert-Jan; Wang, Zhiyue J; Chu, Zili D; Haymond, Morey; Sauer, Pieter J J; Sunehag, Agneta L

2018-06-15

Hispanic adolescent girls with normal BMI frequently have high body fat %. Without knowledge of body fat content and distribution, their risk for metabolic complications is unknown. We measured metabolic risk indicators and abdominal fat distribution in post-pubertal Hispanic adolescent girls with Normal BMI (N-BMI: BMI < 85th percentile) and compared these indicators between girls with Normal BMI and High Fat content (N-BMI-HF: body fat ≥ 27%; n = 15) and Normal BMI and Normal Fat content (N-BMI-NF: body fat < 27%; n = 8). Plasma concentrations of glucose, insulin, adiponectin, leptin and Hs-CRP were determined. Insulin resistance was calculated using an oral glucose tolerance test. Body fat % was measured by DXA and subcutaneous, visceral and hepatic fat by MRI/MRS. The N-BMI-HF girls had increased abdominal and hepatic fat content and increased insulin resistance, plasma leptin and Hs-CRP concentrations ( p < 0.05) as compared to their N-BMI-NF counterparts. In N-BMI girls, insulin resistance, plasma insulin and leptin correlated with BMI and body fat % ( p < 0.05). This research confirms the necessity of the development of BMI and body fat % cut-off criteria per sex, age and racial/ethnic group based on metabolic risk factors to optimize the effectiveness of metabolic risk screening procedures.

Diagnosing and Mapping Pulmonary Emphysema on X-Ray Projection Images: Incremental Value of Grating-Based X-Ray Dark-Field Imaging

PubMed Central

Meinel, Felix G.; Schwab, Felix; Schleede, Simone; Bech, Martin; Herzen, Julia; Achterhold, Klaus; Auweter, Sigrid; Bamberg, Fabian; Yildirim, Ali Ö.; Bohla, Alexander; Eickelberg, Oliver; Loewen, Rod; Gifford, Martin; Ruth, Ronald; Reiser, Maximilian F.; Pfeiffer, Franz; Nikolaou, Konstantin

2013-01-01

Purpose To assess whether grating-based X-ray dark-field imaging can increase the sensitivity of X-ray projection images in the diagnosis of pulmonary emphysema and allow for a more accurate assessment of emphysema distribution. Materials and Methods Lungs from three mice with pulmonary emphysema and three healthy mice were imaged ex vivo using a laser-driven compact synchrotron X-ray source. Median signal intensities of transmission (T), dark-field (V) and a combined parameter (normalized scatter) were compared between emphysema and control group. To determine the diagnostic value of each parameter in differentiating between healthy and emphysematous lung tissue, a receiver-operating-characteristic (ROC) curve analysis was performed both on a per-pixel and a per-individual basis. Parametric maps of emphysema distribution were generated using transmission, dark-field and normalized scatter signal and correlated with histopathology. Results Transmission values relative to water were higher for emphysematous lungs than for control lungs (1.11 vs. 1.06, p<0.001). There was no difference in median dark-field signal intensities between both groups (0.66 vs. 0.66). Median normalized scatter was significantly lower in the emphysematous lungs compared to controls (4.9 vs. 10.8, p<0.001), and was the best parameter for differentiation of healthy vs. emphysematous lung tissue. In a per-pixel analysis, the area under the ROC curve (AUC) for the normalized scatter value was significantly higher than for transmission (0.86 vs. 0.78, p<0.001) and dark-field value (0.86 vs. 0.52, p<0.001) alone. Normalized scatter showed very high sensitivity for a wide range of specificity values (94% sensitivity at 75% specificity). Using the normalized scatter signal to display the regional distribution of emphysema provides color-coded parametric maps, which show the best correlation with histopathology. Conclusion In a murine model, the complementary information provided by X-ray transmission and dark-field images adds incremental diagnostic value in detecting pulmonary emphysema and visualizing its regional distribution as compared to conventional X-ray projections. PMID:23555692

Diagnosing and mapping pulmonary emphysema on X-ray projection images: incremental value of grating-based X-ray dark-field imaging.

PubMed

Meinel, Felix G; Schwab, Felix; Schleede, Simone; Bech, Martin; Herzen, Julia; Achterhold, Klaus; Auweter, Sigrid; Bamberg, Fabian; Yildirim, Ali Ö; Bohla, Alexander; Eickelberg, Oliver; Loewen, Rod; Gifford, Martin; Ruth, Ronald; Reiser, Maximilian F; Pfeiffer, Franz; Nikolaou, Konstantin

2013-01-01

To assess whether grating-based X-ray dark-field imaging can increase the sensitivity of X-ray projection images in the diagnosis of pulmonary emphysema and allow for a more accurate assessment of emphysema distribution. Lungs from three mice with pulmonary emphysema and three healthy mice were imaged ex vivo using a laser-driven compact synchrotron X-ray source. Median signal intensities of transmission (T), dark-field (V) and a combined parameter (normalized scatter) were compared between emphysema and control group. To determine the diagnostic value of each parameter in differentiating between healthy and emphysematous lung tissue, a receiver-operating-characteristic (ROC) curve analysis was performed both on a per-pixel and a per-individual basis. Parametric maps of emphysema distribution were generated using transmission, dark-field and normalized scatter signal and correlated with histopathology. Transmission values relative to water were higher for emphysematous lungs than for control lungs (1.11 vs. 1.06, p<0.001). There was no difference in median dark-field signal intensities between both groups (0.66 vs. 0.66). Median normalized scatter was significantly lower in the emphysematous lungs compared to controls (4.9 vs. 10.8, p<0.001), and was the best parameter for differentiation of healthy vs. emphysematous lung tissue. In a per-pixel analysis, the area under the ROC curve (AUC) for the normalized scatter value was significantly higher than for transmission (0.86 vs. 0.78, p<0.001) and dark-field value (0.86 vs. 0.52, p<0.001) alone. Normalized scatter showed very high sensitivity for a wide range of specificity values (94% sensitivity at 75% specificity). Using the normalized scatter signal to display the regional distribution of emphysema provides color-coded parametric maps, which show the best correlation with histopathology. In a murine model, the complementary information provided by X-ray transmission and dark-field images adds incremental diagnostic value in detecting pulmonary emphysema and visualizing its regional distribution as compared to conventional X-ray projections.

Robust Bayesian Factor Analysis

ERIC Educational Resources Information Center

Hayashi, Kentaro; Yuan, Ke-Hai

2003-01-01

Bayesian factor analysis (BFA) assumes the normal distribution of the current sample conditional on the parameters. Practical data in social and behavioral sciences typically have significant skewness and kurtosis. If the normality assumption is not attainable, the posterior analysis will be inaccurate, although the BFA depends less on the current…

16 CFR 1015.1 - Purpose and scope.

Code of Federal Regulations, 2014 CFR

2014-01-01

..., magazines, or other reference material; or documents routinely distributed by the Commission in the normal course of business such as copies of Federal Register notices, pamphlets, and laws. Official records... to the public in the normal course of business will continue to be furnished to the public by...

16 CFR 1015.1 - Purpose and scope.

Code of Federal Regulations, 2011 CFR

2011-01-01

..., magazines, or other reference material; or documents routinely distributed by the Commission in the normal course of business such as copies of Federal Register notices, pamphlets, and laws. Official records... to the public in the normal course of business will continue to be furnished to the public by...

16 CFR 1015.1 - Purpose and scope.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., magazines, or other reference material; or documents routinely distributed by the Commission in the normal course of business such as copies of Federal Register notices, pamphlets, and laws. Official records... to the public in the normal course of business will continue to be furnished to the public by...

16 CFR 1015.1 - Purpose and scope.

Code of Federal Regulations, 2012 CFR

2012-01-01

..., magazines, or other reference material; or documents routinely distributed by the Commission in the normal course of business such as copies of Federal Register notices, pamphlets, and laws. Official records... to the public in the normal course of business will continue to be furnished to the public by...

Effect of Box-Cox transformation on power of Haseman-Elston and maximum-likelihood variance components tests to detect quantitative trait Loci.

PubMed

Etzel, C J; Shete, S; Beasley, T M; Fernandez, J R; Allison, D B; Amos, C I

2003-01-01

Non-normality of the phenotypic distribution can affect power to detect quantitative trait loci in sib pair studies. Previously, we observed that Winsorizing the sib pair phenotypes increased the power of quantitative trait locus (QTL) detection for both Haseman-Elston (HE) least-squares tests [Hum Hered 2002;53:59-67] and maximum likelihood-based variance components (MLVC) analysis [Behav Genet (in press)]. Winsorizing the phenotypes led to a slight increase in type 1 error in H-E tests and a slight decrease in type I error for MLVC analysis. Herein, we considered transforming the sib pair phenotypes using the Box-Cox family of transformations. Data were simulated for normal and non-normal (skewed and kurtic) distributions. Phenotypic values were replaced by Box-Cox transformed values. Twenty thousand replications were performed for three H-E tests of linkage and the likelihood ratio test (LRT), the Wald test and other robust versions based on the MLVC method. We calculated the relative nominal inflation rate as the ratio of observed empirical type 1 error divided by the set alpha level (5, 1 and 0.1% alpha levels). MLVC tests applied to non-normal data had inflated type I errors (rate ratio greater than 1.0), which were controlled best by Box-Cox transformation and to a lesser degree by Winsorizing. For example, for non-transformed, skewed phenotypes (derived from a chi2 distribution with 2 degrees of freedom), the rates of empirical type 1 error with respect to set alpha level=0.01 were 0.80, 4.35 and 7.33 for the original H-E test, LRT and Wald test, respectively. For the same alpha level=0.01, these rates were 1.12, 3.095 and 4.088 after Winsorizing and 0.723, 1.195 and 1.905 after Box-Cox transformation. Winsorizing reduced inflated error rates for the leptokurtic distribution (derived from a Laplace distribution with mean 0 and variance 8). Further, power (adjusted for empirical type 1 error) at the 0.01 alpha level ranged from 4.7 to 17.3% across all tests using the non-transformed, skewed phenotypes, from 7.5 to 20.1% after Winsorizing and from 12.6 to 33.2% after Box-Cox transformation. Likewise, power (adjusted for empirical type 1 error) using leptokurtic phenotypes at the 0.01 alpha level ranged from 4.4 to 12.5% across all tests with no transformation, from 7 to 19.2% after Winsorizing and from 4.5 to 13.8% after Box-Cox transformation. Thus the Box-Cox transformation apparently provided the best type 1 error control and maximal power among the procedures we considered for analyzing a non-normal, skewed distribution (chi2) while Winzorizing worked best for the non-normal, kurtic distribution (Laplace). We repeated the same simulations using a larger sample size (200 sib pairs) and found similar results. Copyright 2003 S. Karger AG, Basel

Effects of adipose tissue distribution on maximum lipid oxidation rate during exercise in normal-weight women.

PubMed

Isacco, L; Thivel, D; Duclos, M; Aucouturier, J; Boisseau, N

2014-06-01

Fat mass localization affects lipid metabolism differently at rest and during exercise in overweight and normal-weight subjects. The aim of this study was to investigate the impact of a low vs high ratio of abdominal to lower-body fat mass (index of adipose tissue distribution) on the exercise intensity (Lipox(max)) that elicits the maximum lipid oxidation rate in normal-weight women. Twenty-one normal-weight women (22.0 ± 0.6 years, 22.3 ± 0.1 kg.m(-2)) were separated into two groups of either a low or high abdominal to lower-body fat mass ratio [L-A/LB (n = 11) or H-A/LB (n = 10), respectively]. Lipox(max) and maximum lipid oxidation rate (MLOR) were determined during a submaximum incremental exercise test. Abdominal and lower-body fat mass were determined from DXA scans. The two groups did not differ in aerobic fitness, total fat mass, or total and localized fat-free mass. Lipox(max) and MLOR were significantly lower in H-A/LB vs L-A/LB women (43 ± 3% VO(2max) vs 54 ± 4% VO(2max), and 4.8 ± 0.6 mg min(-1)kg FFM(-1)vs 8.4 ± 0.9 mg min(-1)kg FFM(-1), respectively; P < 0.001). Total and abdominal fat mass measurements were negatively associated with Lipox(max) (r = -0.57 and r = -0.64, respectively; P < 0.01) and MLOR [r = -0.63 (P < 0.01) and r = -0.76 (P < 0.001), respectively]. These findings indicate that, in normal-weight women, a predominantly abdominal fat mass distribution compared with a predominantly peripheral fat mass distribution is associated with a lower capacity to maximize lipid oxidation during exercise, as evidenced by their lower Lipox(max) and MLOR. Copyright © 2014 Elsevier Masson SAS. All rights reserved.

Normal Weight Obese syndrome: role of single nucleotide polymorphism of IL-1 5Ralpha and MTHFR 677C-->T genes in the relationship between body composition and resting metabolic rate.

PubMed

Di Renzo, L; Bigioni, M; Bottini, F G; Del Gobbo, V; Premrov, M G; Cianci, R; De Lorenzo, A

2006-01-01

We have identified a subset of metabolically obese, but normal weight individuals, with potentially increased risks of developing the metabolic syndrome, despite their normal body mass index. We determined the relationship among body fat distribution, resting metabolic rate (RMR), total body water amount (%TBW), selected gene polymorphism on interleukin-15 receptor-alpha (IL-15Ralpha) and methylenetetrahydrofolate reductase 677C-->T (MTHFR 677C-->T), to distinguish normal weight obese (NWO) from nonobese with a normal metabolic profile and obese individuals. We analysed anthropometric variables, body composition by Dual energy X-ray Absorptiometry (DXA), RMR by indirect calorimetry, %TBW by bioimpedence analysis (BIA), MTHFR 677C-->T and IL-15Ralpha genotypes of 128 clinically healthy Caucasian individuals. We compared a group of female, defined as NWO and characterised by a BMI < or = 25 kg/m(2) and FM > or = 30% with groups of others female, and males, represented by nonobese with a BMI < or = 25 kg/m(2) and FM < or = 30%, and preobese-obese individuals with BMI > or = 25 kg/m(2) and %FM > or = 30%; none of the males was classified as NWO. Significant correlations were found among body fat mass distribution, metabolic variables, percentage of total body water distribution and selected genetic variations. The variables that contributed significantly to the separation of classes were body tissue (Tissue), %TBW, RMR, the volumes of both oxygen (VO2) and carbon dioxide (VCO2). The distribution of MTHFR 677C-->T and IL-15 genotypes was significantly different between classes. Our data highlight that NWO individuals showed a significant relationship between the decrease in the basal metabolism (RMR), body fat mass increasing and total water amount. Possession of wild type homozygotes genotypes regarding IL-15Ralpha cytokine and 677C-->T MTHFR enzyme characterised NWO individuals.

Inherited discontinuities and fault kinematics of a multiphase, non-colinear extensional setting: Subsurface observations from the South Flank of the Golfo San Jorge basin, Patagonia

NASA Astrophysics Data System (ADS)

Paredes, José Matildo; Aguiar, Mariana; Ansa, Andrés; Giordano, Sergio; Ledesma, Mario; Tejada, Silvia

2018-01-01

We use three-dimensional (3D) seismic reflection data to analyze the structural style, fault kinematics and growth fault mechanisms of non-colinear normal fault systems in the South Flank of the Golfo San Jorge basin, central Patagonia. Pre-existing structural fabrics in the basement of the South Flank show NW-SE and NE-SW oriented faults. They control the location and geometry of wedge-shaped half grabens from the "main synrift phase" infilled with Middle Jurassic volcanic-volcaniclastic rocks and lacustrine units of Late Jurassic to Early Cretaceous age. The NE-striking, basement-involved normal faults resulted in the rapid establishment of fault lenght, followed by gradual increasing in displacement, and minor reactivation during subsequent extensional phases; NW-striking normal faults are characterized by fault segments that propagated laterally during the "main rifting phase", being subsequently reactivated during succesive extensional phases. The Aptian-Campanian Chubut Group is a continental succession up to 4 km thick associated to the "second rifting stage", characterized by propagation and linkage of W-E to WNW-ESE fault segments that increase their lenght and displacement in several extensional phases, recognized by detailed measurement of current throw distribution of selected seismic horizons along fault surfaces. Strain is distributed in an array of sub-parallel normal faults oriented normal to the extension direction. A Late Cretaceous-Paleogene (pre-late Eocene) extensional event is characterized by high-angle, NNW-SSE to NNE-SSW grabens coeval with intraplate alkali basaltic volcanism, evidencing clockwise rotation of the stress field following a ∼W-E extension direction. We demonstrate differences in growth fault mechanisms of non-colinear fault populations, and highlight the importance of follow a systematic approach to the analysis of fault geometry and throw distribution in a fault network, in order to understand temporal-spatial variations in the coeval topography, potential structural traps, and distribution of oil-bearing sandstone reservoirs.

Deformation structure analysis of material at fatigue on the basis of the vector field

NASA Astrophysics Data System (ADS)

Kibitkin, Vladimir V.; Solodushkin, Andrey I.; Pleshanov, Vasily S.

2017-12-01

In the paper, spatial distributions of deformation, circulation, and shear amplitudes and shear angles are obtained from the displacement vector field measured by the DIC technique. This vector field and its characteristics of shears and vortices are given as an example of such approach. The basic formulae are also given. The experiment shows that honeycomb deformation structures can arise in the center of a macrovortex at developed plastic flow. The spatial distribution of local circulation and shears is discovered, which coincides with the deformation structure but their amplitudes are different. The analysis proves that the spatial distribution of shear angles is a result of maximum tangential and normal stresses. The anticlockwise circulation of most local vortices obeys the normal Gaussian law in the area of interest.

Robust and efficient estimation with weighted composite quantile regression

NASA Astrophysics Data System (ADS)

Jiang, Xuejun; Li, Jingzhi; Xia, Tian; Yan, Wanfeng

2016-09-01

In this paper we introduce a weighted composite quantile regression (CQR) estimation approach and study its application in nonlinear models such as exponential models and ARCH-type models. The weighted CQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator (MLE) for a variety of error distributions including the normal, mixed-normal, Student's t, Cauchy distributions, etc. We also suggest an algorithm for the fast implementation of the proposed methodology. Simulations are carried out to compare the performance of different estimators, and the proposed approach is used to analyze the daily S&P 500 Composite index, which verifies the effectiveness and efficiency of our theoretical results.

Robust LOD scores for variance component-based linkage analysis.

PubMed

Blangero, J; Williams, J T; Almasy, L

2000-01-01

The variance component method is now widely used for linkage analysis of quantitative traits. Although this approach offers many advantages, the importance of the underlying assumption of multivariate normality of the trait distribution within pedigrees has not been studied extensively. Simulation studies have shown that traits with leptokurtic distributions yield linkage test statistics that exhibit excessive Type I error when analyzed naively. We derive analytical formulae relating the deviation from the expected asymptotic distribution of the lod score to the kurtosis and total heritability of the quantitative trait. A simple correction constant yields a robust lod score for any deviation from normality and for any pedigree structure, and effectively eliminates the problem of inflated Type I error due to misspecification of the underlying probability model in variance component-based linkage analysis.

Directional data analysis under the general projected normal distribution

PubMed Central

Wang, Fangpo; Gelfand, Alan E.

2013-01-01

The projected normal distribution is an under-utilized model for explaining directional data. In particular, the general version provides flexibility, e.g., asymmetry and possible bimodality along with convenient regression specification. Here, we clarify the properties of this general class. We also develop fully Bayesian hierarchical models for analyzing circular data using this class. We show how they can be fit using MCMC methods with suitable latent variables. We show how posterior inference for distributional features such as the angular mean direction and concentration can be implemented as well as how prediction within the regression setting can be handled. With regard to model comparison, we argue for an out-of-sample approach using both a predictive likelihood scoring loss criterion and a cumulative rank probability score criterion. PMID:24046539

Lognormal Behavior of the Size Distributions of Animation Characters

NASA Astrophysics Data System (ADS)

Yamamoto, Ken

This study investigates the statistical property of the character sizes of animation, superhero series, and video game. By using online databases of Pokémon (video game) and Power Rangers (superhero series), the height and weight distributions are constructed, and we find that the weight distributions of Pokémon and Zords (robots in Power Rangers) follow the lognormal distribution in common. For the theoretical mechanism of this lognormal behavior, the combination of the normal distribution and the Weber-Fechner law is proposed.

Ejected Particle Size Distributions from Shocked Metal Surfaces

DOE PAGES

Schauer, M. M.; Buttler, W. T.; Frayer, D. K.; ...

2017-04-12

Here, we present size distributions for particles ejected from features machined onto the surface of shocked Sn targets. The functional form of the size distributions is assumed to be log-normal, and the characteristic parameters of the distribution are extracted from the measured angular distribution of light scattered from a laser beam incident on the ejected particles. We also found strong evidence for a bimodal distribution of particle sizes with smaller particles evolved from features machined into the target surface and larger particles being produced at the edges of these features.

Ejected Particle Size Distributions from Shocked Metal Surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schauer, M. M.; Buttler, W. T.; Frayer, D. K.

Here, we present size distributions for particles ejected from features machined onto the surface of shocked Sn targets. The functional form of the size distributions is assumed to be log-normal, and the characteristic parameters of the distribution are extracted from the measured angular distribution of light scattered from a laser beam incident on the ejected particles. We also found strong evidence for a bimodal distribution of particle sizes with smaller particles evolved from features machined into the target surface and larger particles being produced at the edges of these features.

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. I - Pressure distribution

NASA Technical Reports Server (NTRS)

Messiter, A. F.

1980-01-01

Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.

Comparison of experimental and theoretical normal-force distributions (including Reynolds number effects) on an ogive-cylinder body at Mach number 1.98

NASA Technical Reports Server (NTRS)

Perkins, Edward W; Jorgensen, Leland H

1956-01-01

Effects of Reynolds number and angle of attack on the pressure distribution and normal-force characteristics of a body of revolution consisting of a fineness ratio 3 ogival nose tangent to a cylindrical afterbody 7 diameters long have been determined. The test Mach number was 1.98 and the angle-of-attack range from 0 degree to 20 degrees. The Reynolds numbers, based on body diameter, were 0.15 x 10(6) and 0.45 x 10(6). The experimental results are compared with theory.

Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface

NASA Astrophysics Data System (ADS)

Volkov, Sergei S.; Vasiliev, Andrey S.; Aizikovich, Sergei M.; Sadyrin, Evgeniy V.

2018-05-01

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided.

Stone former urine proteome demonstrates a cationic shift in protein distribution compared to normal.

PubMed

Kolbach-Mandel, Ann M; Mandel, Neil S; Hoffmann, Brian R; Kleinman, Jack G; Wesson, Jeffrey A

2017-08-01

Many urine proteins are found in calcium oxalate stones, yet decades of research have failed to define the role of urine proteins in stone formation. This urine proteomic study compares the relative amounts of abundant urine proteins between idiopathic calcium oxalate stone forming and non-stone forming (normal) cohorts to identify differences that might correlate with disease. Random mid-morning urine samples were collected following informed consent from 25 stone formers and 14 normal individuals. Proteins were isolated from urine using ultrafiltration. Urine proteomes for each sample were characterized using label-free spectral counting mass spectrometry, so that urine protein relative abundances could be compared between the two populations. A total of 407 unique proteins were identified with the 38 predominant proteins accounting for >82% of all sample spectral counts. The most highly abundant proteins were equivalent in stone formers and normals, though significant differences were observed in a few moderate abundance proteins (immunoglobulins, transferrin, and epidermal growth factor), accounting for 13 and 10% of the spectral counts, respectively. These proteins contributed to a cationic shift in protein distribution in stone formers compared to normals (22% vs. 18%, p = 0.04). Our data showing only small differences in moderate abundance proteins suggest that no single protein controls stone formation. Observed increases in immunoglobulins and transferrin suggest increased inflammatory activity in stone formers, but cannot distinguish cause from effect in stone formation. The observed cationic shift in protein distribution would diminish protein charge stabilization, which could lead to protein aggregation and increased risk for crystal aggregation.

UPLC-MS method for quantification of pterostilbene and its application to comparative study of bioavailability and tissue distribution in normal and Lewis lung carcinoma bearing mice.

PubMed

Deng, Li; Li, Yongzhi; Zhang, Xinshi; Chen, Bo; Deng, Yulin; Li, Yujuan

2015-10-10

A UPLC-MS method was developed for determination of pterostilbene (PTS) in plasma and tissues of mice. PTS was separated on Agilent Zorbax XDB-C18 column (50 × 2.1 mm, 1.8 μm) with gradient mobile phase at the flow rate of 0.2 ml/min. The detection was performed by negative ion electrospray ionization in multiple reaction monitoring mode. The linear calibration curve of PTS in mouse plasma and tissues ranged from 1.0 to 5000 and 0.50 to 500 ng/ml (r(2)>0.9979), respectively, with lowest limits of quantification (LLOQ) were between 0.5 and 2.0 ng/ml, respectively. The accuracy and precision of the assay were satisfactory. The validated method was applied to the study of bioavailability and tissue distribution of PTS in normal and Lewis lung carcinoma (LLC) bearing mice. The bioavailability of PTS (dose 14, 28 and 56 mg/kg) in normal mice were 11.9%, 13.9% and 26.4%, respectively; and the maximum level (82.1 ± 14.2 μg/g) was found in stomach (dose 28 mg/kg). The bioavailability, peak concentration (Cmax), time to peak concentration (Tmax) of PTS in LLC mice was increased compared with normal mice. The results indicated the UPLC-MS method is reliable and bioavailability and tissue distribution of PTS in normal and LLC mice were dramatically different. Copyright © 2015 Elsevier B.V. All rights reserved.

Applications of multiscale change point detections to monthly stream flow and rainfall in Xijiang River in southern China, part I: correlation and variance

NASA Astrophysics Data System (ADS)

Zhu, Yuxiang; Jiang, Jianmin; Huang, Changxing; Chen, Yongqin David; Zhang, Qiang

2018-04-01

This article, as part I, introduces three algorithms and applies them to both series of the monthly stream flow and rainfall in Xijiang River, southern China. The three algorithms include (1) normalization of probability distribution, (2) scanning U test for change points in correlation between two time series, and (3) scanning F-test for change points in variances. The normalization algorithm adopts the quantile method to normalize data from a non-normal into the normal probability distribution. The scanning U test and F-test have three common features: grafting the classical statistics onto the wavelet algorithm, adding corrections for independence into each statistic criteria at given confidence respectively, and being almost objective and automatic detection on multiscale time scales. In addition, the coherency analyses between two series are also carried out for changes in variance. The application results show that the changes of the monthly discharge are still controlled by natural precipitation variations in Xijiang's fluvial system. Human activities disturbed the ecological balance perhaps in certain content and in shorter spells but did not violate the natural relationships of correlation and variance changes so far.

Multivariate normality

NASA Technical Reports Server (NTRS)

Crutcher, H. L.; Falls, L. W.

1976-01-01

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Molecular analysis of tumor margins by MALDI mass spectrometry in renal carcinoma.

PubMed

Oppenheimer, Stacey R; Mi, Deming; Sanders, Melinda E; Caprioli, Richard M

2010-05-07

The rate of tumor recurrence post resection suggests that there are underlying molecular changes in nearby histologically normal tissue that go undetected by conventional diagnostic methods that utilize contrast agents and immunohistochemistry. MALDI MS is a molecular technology that has the specificity and sensitivity to monitor and identify molecular species indicative of these changes. The current study utilizes this technology to assess molecular distributions within a tumor and adjacent normal tissue in clear cell renal cell carcinoma biopsies. Results indicate that the histologically normal tissue adjacent to the tumor expresses many of the molecular characteristics of the tumor. Proteins of the mitochondrial electron transport system are examples of such distributions. This work demonstrates the utility of MALDI MS for the analysis of tumor tissue in the elucidation of aberrant molecular changes in the tumor microenvironment.

Alpha, delta and theta rhythms in a neural net model. Comparison with MEG data.

PubMed

Kotini, A; Anninos, P

2016-01-07

The aim of this study is to provide information regarding the comparison of a neural model to MEG measurements. Our study population consisted of 10 epileptic patients and 10 normal subjects. The epileptic patients had high MEG amplitudes characterized with θ (4-7 Hz) or δ (2-3 Hz) rhythms and absence of α-rhythm (8-13 Hz). The statistical analysis of such activities corresponded to Poisson distribution. Conversely, the MEG from normal subjects had low amplitudes, higher frequencies and presence of α-rhythm (8-13 Hz). Such activities were not synchronized and their distributions were Gauss. These findings were in agreement with our theoretical neural model. The comparison of the neural network with MEG data provides information about the status of brain function in epileptic and normal states. Copyright © 2015 Elsevier Ltd. All rights reserved.

Sera of IgA nephropathy patients contain a heterogeneous population of relatively cationic alpha-heavy chains.

PubMed

Shuib, A S; Chua, C T; Hashim, O H

1998-01-01

Sera of IgA nephropathy (IgAN) patients and normal subjects were analysed by two-dimensional (2-D) gel electrophoresis. Densitometric analysis of the 2-D gels of IgAN patients and normal subjects revealed that their protein maps were comparable. There was no shift of pI values in the major alpha-heavy chain spots. However, the volume of the alpha-heavy chain bands were differently distributed. Distribution was significantly lower at the anionic region in IgAN patients (mean anionic:cationic ratio of 1.184 +/- 0.311) as compared to normal healthy controls (mean anionic:cationic ratio of 2.139 +/- 0.538). Our data are in support of the previously reported findings that IgA1 of IgAN patients were lacking in sialic acid residues.

Factoring handedness data: II. Geschwind's multidimensional hypothesis.

PubMed

Messinger, H B; Messinger, M I

1996-06-01

The challenge in this journal by Peters and Murphy to the validity of two published factor analyses of handedness data because of bimodality was dealt with in Part I by identifying measures to normalize the handedness item distributions. A new survey using Oldfield's questionnaire format had 38 bell-shaped (unimodal) handedness-item distributions and 11 that were only marginally bimodal out of the 55 items used in Geschwind's 1986 study. Yet they were still non-normal and the factor analysis was unsatisfactory; bimodality is not the only problem. By choosing a transformation for each item that was optimal as assessed by D'Agostino's K2 statistic, all but two items could be normalized. Seven factors were derived that showed high congruence between maximum likelihood and principal components extractions before and after varimax rotation. Geschwind's assertion that handedness is not unidimensional is therefore supported.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harner, E.J.; Gilfillan, E.S.

Two large shoreline assessment studies conducted in 1990 in Prince William Sound, Alaska, after the Exxon Valdez oil spill used different design strategies to determine the impact of oiling on shoreline biota. One of the studies, the Coastal Habitat Injury Assessment (CHIA) conducted for the Exxon Valdez Oil Spill Council, used matched pairs of sites, normal population distributions for biota, and meta-analysis. The power of the CHIA study to detect oiling impacts depends on being able to identify and select appropriate pairs of sites for comparison. The CHIA study also increased the oiling signal by focusing on moderate to heavilymore » oiled sites. The Shoreline Ecology Program (SEP), conducted for Exxon, used a stratified-random-sampling study design, normal and non-normal population distributions and covariates. The SEP study was able to detect oiling impacts by using a sufficient number of sites and widely spaced transects.« less

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

Interactions of satellite-speed helium atoms with satellite surfaces. 3: Drag coefficients from spatial and energy distributions of reflected helium atoms

NASA Technical Reports Server (NTRS)

Sharma, P. K.; Knuth, E. L.

1977-01-01

Spatial and energy distributions of helium atoms scattered from an anodized 1235-0 aluminum surface as well as the tangential and normal momentum accommodation coefficients calculated from these distributions are reported. A procedure for calculating drag coefficients from measured values of spatial and energy distributions is given. The drag coefficient calculated for a 6061 T-6 aluminum sphere is included.

16 CFR § 1015.1 - Purpose and scope.

Code of Federal Regulations, 2013 CFR

2013-01-01

... property; books, magazines, or other reference material; or documents routinely distributed by the Commission in the normal course of business such as copies of Federal Register notices, pamphlets, and laws... to the public in the normal course of business will continue to be furnished to the public by...

14 CFR 27.321 - General.

Code of Federal Regulations, 2010 CFR

2010-01-01

... STANDARDS: NORMAL CATEGORY ROTORCRAFT Strength Requirements Flight Loads § 27.321 General. (a) The flight load factor must be assumed to act normal to the longitudinal axis of the rotorcraft, and to be equal... from the design minimum weight to the design maximum weight; and (2) With any practical distribution of...

Analysis of orthotropic beams

Treesearch

Jen Y. Liu; S. Cheng

1979-01-01

A plane-stress analysis of orthotropic or isotropic beams is presented. The loading conditions considered are: (1) a concentrated normal load arbitrarily located on the beam, and (2) a distributed normal load covering an arbitrary length of the beam. exhibit close agreement with existing experimental data from Sitka spruce beams. Other loading conditions can similarly...

Local Influence and Robust Procedures for Mediation Analysis

ERIC Educational Resources Information Center

Zu, Jiyun; Yuan, Ke-Hai

2010-01-01

Existing studies of mediation models have been limited to normal-theory maximum likelihood (ML). Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods generally lead to inefficient or biased parameter estimates. Consequently, the conclusions from a mediation analysis…

The Best and the Rest: Revisiting the Norm of Normality of Individual Performance

ERIC Educational Resources Information Center

O'Boyle, Ernest, Jr.; Aguinis, Herman

2012-01-01

We revisit a long-held assumption in human resource management, organizational behavior, and industrial and organizational psychology that individual performance follows a Gaussian (normal) distribution. We conducted 5 studies involving 198 samples including 633,263 researchers, entertainers, politicians, and amateur and professional athletes.…

A product Pearson-type VII density distribution

NASA Astrophysics Data System (ADS)

Nadarajah, Saralees; Kotz, Samuel

2008-01-01

The Pearson-type VII distributions (containing the Student's t distributions) are becoming increasing prominent and are being considered as competitors to the normal distribution. Motivated by real examples in decision sciences, Bayesian statistics, probability theory and Physics, a new Pearson-type VII distribution is introduced by taking the product of two Pearson-type VII pdfs. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to a Bayesian testing problem is illustrated.

Distribution and function of the peptide transporter PEPT2 in normal and cystic fibrosis human lung.

PubMed

Groneberg, D A; Eynott, P R; Döring, F; Dinh, Q Thai; Oates, T; Barnes, P J; Chung, K F; Daniel, H; Fischer, A

2002-01-01

Aerosol administration of peptide based drugs has an important role in the treatment of various pulmonary and systemic diseases. The characterisation of pulmonary peptide transport pathways can lead to new strategies in aerosol drug treatment. Immunohistochemistry and ex vivo uptake studies were established to assess the distribution and activity of the beta-lactam transporting high affinity proton coupled peptide transporter PEPT2 in normal and cystic fibrosis human airway tissue. PEPT2 immunoreactivity in normal human airways was localised to cells of the tracheal and bronchial epithelium and the endothelium of small vessels. In peripheral lung immunoreactivity was restricted to type II pneumocytes. In sections of cystic fibrosis lung a similar pattern of distribution was obtained with signals localised to endothelial cells, airway epithelium, and type II pneumocytes. Functional ex vivo uptake studies with fresh lung specimens led to an uptake of the fluorophore conjugated dipeptide derivative D-Ala-L-Lys-AMCA into bronchial epithelial cells and type II pneumocytes. This uptake was competitively inhibited by dipeptides and cephalosporins but not ACE inhibitors, indicating a substrate specificity as described for PEPT2. These findings provide evidence for the expression and function of the peptide transporter PEPT2 in the normal and cystic fibrosis human respiratory tract and suggest that PEPT2 is likely to play a role in the transport of pulmonary peptides and peptidomimetics.

Distribution and function of the peptide transporter PEPT2 in normal and cystic fibrosis human lung

PubMed Central

Groneberg, D; Eynott, P; Doring, F; Thai, D; Oates, T; Barnes, P; Chung, K; Daniel, H; Fischer, A

2002-01-01

Background: Aerosol administration of peptide based drugs has an important role in the treatment of various pulmonary and systemic diseases. The characterisation of pulmonary peptide transport pathways can lead to new strategies in aerosol drug treatment. Methods: Immunohistochemistry and ex vivo uptake studies were established to assess the distribution and activity of the ß-lactam transporting high affinity proton coupled peptide transporter PEPT2 in normal and cystic fibrosis human airway tissue. Results: PEPT2 immunoreactivity in normal human airways was localised to cells of the tracheal and bronchial epithelium and the endothelium of small vessels. In peripheral lung immunoreactivity was restricted to type II pneumocytes. In sections of cystic fibrosis lung a similar pattern of distribution was obtained with signals localised to endothelial cells, airway epithelium, and type II pneumocytes. Functional ex vivo uptake studies with fresh lung specimens led to an uptake of the fluorophore conjugated dipeptide derivative D-Ala-L-Lys-AMCA into bronchial epithelial cells and type II pneumocytes. This uptake was competitively inhibited by dipeptides and cephalosporins but not ACE inhibitors, indicating a substrate specificity as described for PEPT2. Conclusions: These findings provide evidence for the expression and function of the peptide transporter PEPT2 in the normal and cystic fibrosis human respiratory tract and suggest that PEPT2 is likely to play a role in the transport of pulmonary peptides and peptidomimetics. PMID:11809991

The Sensitivity of Parameter Estimates to the Latent Ability Distribution. Research Report. ETS RR-11-40

ERIC Educational Resources Information Center

Xu, Xueli; Jia, Yue

2011-01-01

Estimation of item response model parameters and ability distribution parameters has been, and will remain, an important topic in the educational testing field. Much research has been dedicated to addressing this task. Some studies have focused on item parameter estimation when the latent ability was assumed to follow a normal distribution,…

On the Distribution of Worker Productivity: The Case for Teacher Effectiveness and Student Achievement. CEDR Working Paper. WP #2016-10

ERIC Educational Resources Information Center

Goldhaber, Dan; Startz, Richard

2016-01-01

It is common to assume that worker productivity is normally distributed, but this assumption is rarely if ever tested. We estimate the distribution of worker productivity where individual productivity is measured with error, using the productivity of elementary school teachers as an example. Proposals to improve teacher productivity often focus on…

High Temperature Silicon Carbide (SiC) Traction Motor Drive

DTIC Science & Technology

2011-08-09

UNCLASSIFIED Distribution Statement A. Approved for public release; distribution is unlimited. UNCLASSIFIED HIGH TEMPERATURE SILICON CARBIDE...be modular and conveniently distributed. Small component size and operation with high - temperature liquid coolant are essential factors in the...these densities, power modules capable of high - temperature operation were developed using SiC normally-off JFETs. This paper will discuss the unique

Noncentral Chi-Square versus Normal Distributions in Describing the Likelihood Ratio Statistic: The Univariate Case and Its Multivariate Implication

ERIC Educational Resources Information Center

Yuan, Ke-Hai

2008-01-01

In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…

14 CFR 27.787 - Cargo and baggage compartments.

Code of Federal Regulations, 2010 CFR

2010-01-01

... AIRCRAFT AIRWORTHINESS STANDARDS: NORMAL CATEGORY ROTORCRAFT Design and Construction Personnel and Cargo... for its placarded maximum weight of contents and for the critical load distributions at the... authorized weight of cargo and baggage at the critical loading distribution. (d) If cargo compartment lamps...

Distribution of the Determinant of the Sample Correlation Matrix: Monte Carlo Type One Error Rates.

ERIC Educational Resources Information Center

Reddon, John R.; And Others

1985-01-01

Computer sampling from a multivariate normal spherical population was used to evaluate the type one error rates for a test of sphericity based on the distribution of the determinant of the sample correlation matrix. (Author/LMO)

Incorporation of a spatial source distribution and a spatial sensor sensitivity in a laser ultrasound propagation model using a streamlined Huygens' principle.

PubMed

Laloš, Jernej; Babnik, Aleš; Možina, Janez; Požar, Tomaž

2016-03-01

The near-field, surface-displacement waveforms in plates are modeled using interwoven concepts of Green's function formalism and streamlined Huygens' principle. Green's functions resemble the building blocks of the sought displacement waveform, superimposed and weighted according to the simplified distribution. The approach incorporates an arbitrary circular spatial source distribution and an arbitrary circular spatial sensitivity in the area probed by the sensor. The displacement histories for uniform, Gaussian and annular normal-force source distributions and the uniform spatial sensor sensitivity are calculated, and the corresponding weight distributions are compared. To demonstrate the applicability of the developed scheme, measurements of laser ultrasound induced solely by the radiation pressure are compared with the calculated waveforms. The ultrasound is induced by laser pulse reflection from the mirror-surface of a glass plate. The measurements show excellent agreement not only with respect to various wave-arrivals but also in the shape of each arrival. Their shape depends on the beam profile of the excitation laser pulse and its corresponding spatial normal-force distribution. Copyright © 2015 Elsevier B.V. All rights reserved.

Distributed gas sensing with optical fibre photothermal interferometry.

PubMed

Lin, Yuechuan; Liu, Fei; He, Xiangge; Jin, Wei; Zhang, Min; Yang, Fan; Ho, Hoi Lut; Tan, Yanzhen; Gu, Lijuan

2017-12-11

We report the first distributed optical fibre trace-gas detection system based on photothermal interferometry (PTI) in a hollow-core photonic bandgap fibre (HC-PBF). Absorption of a modulated pump propagating in the gas-filled HC-PBF generates distributed phase modulation along the fibre, which is detected by a dual-pulse heterodyne phase-sensitive optical time-domain reflectometry (OTDR) system. Quasi-distributed sensing experiment with two 28-meter-long HC-PBF sensing sections connected by single-mode transmission fibres demonstrated a limit of detection (LOD) of ∼10 ppb acetylene with a pump power level of 55 mW and an effective noise bandwidth (ENBW) of 0.01 Hz, corresponding to a normalized detection limit of 5.5ppb⋅W/Hz. Distributed sensing experiment over a 200-meter-long sensing cable made of serially connected HC-PBFs demonstrated a LOD of ∼ 5 ppm with 62.5 mW peak pump power and 11.8 Hz ENBW, or a normalized detection limit of 312ppb⋅W/Hz. The spatial resolution of the current distributed detection system is limited to ∼ 30 m, but it is possible to reduce down to 1 meter or smaller by optimizing the phase detection system.

Evaluation of regulatory variation and theoretical health risk for pesticide maximum residue limits in food.

PubMed

Li, Zijian

2018-08-01

To evaluate whether pesticide maximum residue limits (MRLs) can protect public health, a deterministic dietary risk assessment of maximum pesticide legal exposure was conducted to convert global MRLs to theoretical maximum dose intake (TMDI) values by estimating the average food intake rate and human body weight for each country. A total of 114 nations (58% of the total nations in the world) and two international organizations, including the European Union (EU) and Codex (WHO) have regulated at least one of the most currently used pesticides in at least one of the most consumed agricultural commodities. In this study, 14 of the most commonly used pesticides and 12 of the most commonly consumed agricultural commodities were identified and selected for analysis. A health risk analysis indicated that nearly 30% of the computed pesticide TMDI values were greater than the acceptable daily intake (ADI) values; however, many nations lack common pesticide MRLs in many commonly consumed foods and other human exposure pathways, such as soil, water, and air were not considered. Normality tests of the TMDI values set indicated that all distributions had a right skewness due to large TMDI clusters at the low end of the distribution, which were caused by some strict pesticide MRLs regulated by the EU (normally a default MRL of 0.01 mg/kg when essential data are missing). The Box-Cox transformation and optimal lambda (λ) were applied to these TMDI distributions, and normality tests of the transformed data set indicated that the power transformed TMDI values of at least eight pesticides presented a normal distribution. It was concluded that unifying strict pesticide MRLs by nations worldwide could significantly skew the distribution of TMDI values to the right, lower the legal exposure to pesticide, and effectively control human health risks. Copyright © 2018 Elsevier Ltd. All rights reserved.

Intra-Individual Response Variability Assessed by Ex-Gaussian Analysis may be a New Endophenotype for Attention-Deficit/Hyperactivity Disorder.

PubMed

Henríquez-Henríquez, Marcela Patricia; Billeke, Pablo; Henríquez, Hugo; Zamorano, Francisco Javier; Rothhammer, Francisco; Aboitiz, Francisco

2014-01-01

Intra-individual variability of response times (RTisv) is considered as potential endophenotype for attentional deficit/hyperactivity disorder (ADHD). Traditional methods for estimating RTisv lose information regarding response times (RTs) distribution along the task, with eventual effects on statistical power. Ex-Gaussian analysis captures the dynamic nature of RTisv, estimating normal and exponential components for RT distribution, with specific phenomenological correlates. Here, we applied ex-Gaussian analysis to explore whether intra-individual variability of RTs agrees with criteria proposed by Gottesman and Gould for endophenotypes. Specifically, we evaluated if normal and/or exponential components of RTs may (a) present the stair-like distribution expected for endophenotypes (ADHD > siblings > typically developing children (TD) without familiar history of ADHD) and (b) represent a phenotypic correlate for previously described genetic risk variants. This is a pilot study including 55 subjects (20 ADHD-discordant sibling-pairs and 15 TD children), all aged between 8 and 13 years. Participants resolved a visual Go/Nogo with 10% Nogo probability. Ex-Gaussian distributions were fitted to individual RT data and compared among the three samples. In order to test whether intra-individual variability may represent a correlate for previously described genetic risk variants, VNTRs at DRD4 and SLC6A3 were identified in all sibling-pairs following standard protocols. Groups were compared adjusting independent general linear models for the exponential and normal components from the ex-Gaussian analysis. Identified trends were confirmed by the non-parametric Jonckheere-Terpstra test. Stair-like distributions were observed for μ (p = 0.036) and σ (p = 0.009). An additional "DRD4-genotype" × "clinical status" interaction was present for τ (p = 0.014) reflecting a possible severity factor. Thus, normal and exponential RTisv components are suitable as ADHD endophenotypes.

On the intrinsic shape of the gamma-ray spectrum for Fermi blazars

NASA Astrophysics Data System (ADS)

Kang, Shi-Ju; Wu, Qingwen; Zheng, Yong-Gang; Yin, Yue; Song, Jia-Li; Zou, Hang; Feng, Jian-Chao; Dong, Ai-Jun; Wu, Zhong-Zu; Zhang, Zhi-Bin; Wu, Lin-Hui

2018-05-01

The curvature of the γ-ray spectrumin blazarsmay reflect the intrinsic distribution of emitting electrons, which will further give some information on the possible acceleration and cooling processes in the emitting region. The γ-ray spectra of Fermi blazars are normally fitted either by a single power-law (PL) or a log-normal (call Logarithmic Parabola, LP) form. The possible reason for this difference is not clear. We statistically explore this issue based on the different observational properties of 1419 Fermi blazars in the 3LAC Clean Sample.We find that the γ-ray flux (100MeV–100GeV) and variability index follow bimodal distributions for PL and LP blazars, where the γ-ray flux and variability index show a positive correlation. However, the distributions of γ-ray luminosity and redshift follow a unimodal distribution. Our results suggest that the bimodal distribution of γ-ray fluxes for LP and PL blazars may not be intrinsic and all blazars may have an intrinsically curved γ-ray spectrum, and the PL spectrum is just caused by the fitting effect due to less photons.

Double stars with wide separations in the AGK3 - II. The wide binaries and the multiple systems*

NASA Astrophysics Data System (ADS)

Halbwachs, J.-L.; Mayor, M.; Udry, S.

2017-02-01

A large observation programme was carried out to measure the radial velocities of the components of a selection of common proper motion (CPM) stars to select the physical binaries. 80 wide binaries (WBs) were detected, and 39 optical pairs were identified. By adding CPM stars with separations close enough to be almost certain that they are physical, a bias-controlled sample of 116 WBs was obtained, and used to derive the distribution of separations from 100 to 30 000 au. The distribution obtained does not match the log-constant distribution, but agrees with the log-normal distribution. The spectroscopic binaries detected among the WB components were used to derive statistical information about the multiple systems. The close binaries in WBs seem to be like those detected in other field stars. As for the WBs, they seem to obey the log-normal distribution of periods. The number of quadruple systems agrees with the no correlation hypothesis; this indicates that an environment conducive to the formation of WBs does not favour the formation of subsystems with periods shorter than 10 yr.

Estimation of value at risk in currency exchange rate portfolio using asymmetric GJR-GARCH Copula

NASA Astrophysics Data System (ADS)

Nurrahmat, Mohamad Husein; Noviyanti, Lienda; Bachrudin, Achmad

2017-03-01

In this study, we discuss the problem in measuring the risk in a portfolio based on value at risk (VaR) using asymmetric GJR-GARCH Copula. The approach based on the consideration that the assumption of normality over time for the return can not be fulfilled, and there is non-linear correlation for dependent model structure among the variables that lead to the estimated VaR be inaccurate. Moreover, the leverage effect also causes the asymmetric effect of dynamic variance and shows the weakness of the GARCH models due to its symmetrical effect on conditional variance. Asymmetric GJR-GARCH models are used to filter the margins while the Copulas are used to link them together into a multivariate distribution. Then, we use copulas to construct flexible multivariate distributions with different marginal and dependence structure, which is led to portfolio joint distribution does not depend on the assumptions of normality and linear correlation. VaR obtained by the analysis with confidence level 95% is 0.005586. This VaR derived from the best Copula model, t-student Copula with marginal distribution of t distribution.

Landscape-scale spatial abundance distributions discriminate core from random components of boreal lake bacterioplankton.

PubMed

Niño-García, Juan Pablo; Ruiz-González, Clara; Del Giorgio, Paul A

2016-12-01

Aquatic bacterial communities harbour thousands of coexisting taxa. To meet the challenge of discriminating between a 'core' and a sporadically occurring 'random' component of these communities, we explored the spatial abundance distribution of individual bacterioplankton taxa across 198 boreal lakes and their associated fluvial networks (188 rivers). We found that all taxa could be grouped into four distinct categories based on model statistical distributions (normal like, bimodal, logistic and lognormal). The distribution patterns across lakes and their associated river networks showed that lake communities are composed of a core of taxa whose distribution appears to be linked to in-lake environmental sorting (normal-like and bimodal categories), and a large fraction of mostly rare bacteria (94% of all taxa) whose presence appears to be largely random and linked to downstream transport in aquatic networks (logistic and lognormal categories). These rare taxa are thus likely to reflect species sorting at upstream locations, providing a perspective of the conditions prevailing in entire aquatic networks rather than only in lakes. © 2016 John Wiley & Sons Ltd/CNRS.

On the Use of the Log-Normal Particle Size Distribution to Characterize Global Rain

NASA Technical Reports Server (NTRS)

Meneghini, Robert; Rincon, Rafael; Liao, Liang

2003-01-01

Although most parameterizations of the drop size distributions (DSD) use the gamma function, there are several advantages to the log-normal form, particularly if we want to characterize the large scale space-time variability of the DSD and rain rate. The advantages of the distribution are twofold: the logarithm of any moment can be expressed as a linear combination of the individual parameters of the distribution; the parameters of the distribution are approximately normally distributed. Since all radar and rainfall-related parameters can be written approximately as a moment of the DSD, the first property allows us to express the logarithm of any radar/rainfall variable as a linear combination of the individual DSD parameters. Another consequence is that any power law relationship between rain rate, reflectivity factor, specific attenuation or water content can be expressed in terms of the covariance matrix of the DSD parameters. The joint-normal property of the DSD parameters has applications to the description of the space-time variation of rainfall in the sense that any radar-rainfall quantity can be specified by the covariance matrix associated with the DSD parameters at two arbitrary space-time points. As such, the parameterization provides a means by which we can use the spaceborne radar-derived DSD parameters to specify in part the covariance matrices globally. However, since satellite observations have coarse temporal sampling, the specification of the temporal covariance must be derived from ancillary measurements and models. Work is presently underway to determine whether the use of instantaneous rain rate data from the TRMM Precipitation Radar can provide good estimates of the spatial correlation in rain rate from data collected in 5(sup 0)x 5(sup 0) x 1 month space-time boxes. To characterize the temporal characteristics of the DSD parameters, disdrometer data are being used from the Wallops Flight Facility site where as many as 4 disdrometers have been used to acquire data over a 2 km path. These data should help quantify the temporal form of the covariance matrix at this site.

Linear energy transfer incorporated intensity modulated proton therapy optimization

NASA Astrophysics Data System (ADS)

Cao, Wenhua; Khabazian, Azin; Yepes, Pablo P.; Lim, Gino; Poenisch, Falk; Grosshans, David R.; Mohan, Radhe

2018-01-01

The purpose of this study was to investigate the feasibility of incorporating linear energy transfer (LET) into the optimization of intensity modulated proton therapy (IMPT) plans. Because increased LET correlates with increased biological effectiveness of protons, high LETs in target volumes and low LETs in critical structures and normal tissues are preferred in an IMPT plan. However, if not explicitly incorporated into the optimization criteria, different IMPT plans may yield similar physical dose distributions but greatly different LET, specifically dose-averaged LET, distributions. Conventionally, the IMPT optimization criteria (or cost function) only includes dose-based objectives in which the relative biological effectiveness (RBE) is assumed to have a constant value of 1.1. In this study, we added LET-based objectives for maximizing LET in target volumes and minimizing LET in critical structures and normal tissues. Due to the fractional programming nature of the resulting model, we used a variable reformulation approach so that the optimization process is computationally equivalent to conventional IMPT optimization. In this study, five brain tumor patients who had been treated with proton therapy at our institution were selected. Two plans were created for each patient based on the proposed LET-incorporated optimization (LETOpt) and the conventional dose-based optimization (DoseOpt). The optimized plans were compared in terms of both dose (assuming a constant RBE of 1.1 as adopted in clinical practice) and LET. Both optimization approaches were able to generate comparable dose distributions. The LET-incorporated optimization achieved not only pronounced reduction of LET values in critical organs, such as brainstem and optic chiasm, but also increased LET in target volumes, compared to the conventional dose-based optimization. However, on occasion, there was a need to tradeoff the acceptability of dose and LET distributions. Our conclusion is that the inclusion of LET-dependent criteria in the IMPT optimization could lead to similar dose distributions as the conventional optimization but superior LET distributions in target volumes and normal tissues. This may have substantial advantages in improving tumor control and reducing normal tissue toxicities.

Size distributions of aerosol and water-soluble ions in Nanjing during a crop residual burning event.

PubMed

Wang, Honglei; Zhu, Bin; Shen, Lijuan; Kang, Hanqing

2012-01-01

To investigate the impact on urban air pollution by crop residual burning outside Nanjing, aerosol concentration, pollution gas concentration, mass concentration, and water-soluble ion size distribution were observed during one event of November 4-9, 2010. Results show that the size distribution of aerosol concentration is bimodal on pollution days and normal days, with peak values at 60-70 and 200-300 nm, respectively. Aerosol concentration is 10(4) cm(-3) x nm(-1) on pollution days. The peak value of spectrum distribution of aerosol concentration on pollution days is 1.5-3.3 times higher than that on a normal day. Crop residual burning has a great impact on the concentration of fine particles. Diurnal variation of aerosol concentration is trimodal on pollution days and normal days, with peak values at 03:00, 09:00 and 19:00 local standard time. The first peak is impacted by meteorological elements, while the second and third peaks are due to human activities, such as rush hour traffic. Crop residual burning has the greatest impact on SO2 concentration, followed by NO2, O3 is hardly affected. The impact of crop residual burning on fine particles (< 2.1 microm) is larger than on coarse particles (> 2.1 microm), thus ion concentration in fine particles is higher than that in coarse particles. Crop residual burning leads to similar increase in all ion components, thus it has a small impact on the water-soluble ions order. Crop residual burning has a strong impact on the size distribution of K+, Cl-, Na+, and F- and has a weak impact on the size distributions of NH4+, Ca2+, NO3- and SO4(2-).

Estimating the extreme low-temperature event using nonparametric methods

NASA Astrophysics Data System (ADS)

D'Silva, Anisha

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. We present a detailed explanation of our One-in-N Algorithm and compare it to the methods using the generalized extreme value distribution, the normal distribution, and the variance-weighted composite distribution. We show that our One-in-N Algorithm estimates the one-in- N low temperature threshold more accurately than the methods using the generalized extreme value distribution, the normal distribution, and the variance-weighted composite distribution according to root mean square error (RMSE) measure at a 5% level of significance. The One-in- N Algorithm is tested by counting the number of times the daily average wind-adjusted temperature is less than or equal to the one-in- N low temperature threshold.

Localization of Cell Wall Polysaccharides in Normal and Compression Wood of Radiata Pine: Relationships with Lignification and Microfibril Orientation1

PubMed Central

Donaldson, Lloyd A.; Knox, J. Paul

2012-01-01

The distribution of noncellulosic polysaccharides in cell walls of tracheids and xylem parenchyma cells in normal and compression wood of Pinus radiata, was examined to determine the relationships with lignification and cellulose microfibril orientation. Using fluorescence microscopy combined with immunocytochemistry, monoclonal antibodies were used to detect xyloglucan (LM15), β(1,4)-galactan (LM5), heteroxylan (LM10 and LM11), and galactoglucomannan (LM21 and LM22). Lignin and crystalline cellulose were localized on the same sections used for immunocytochemistry by autofluorescence and polarized light microscopy, respectively. Changes in the distribution of noncellulosic polysaccharides between normal and compression wood were associated with changes in lignin distribution. Increased lignification of compression wood secondary walls was associated with novel deposition of β(1,4)-galactan and with reduced amounts of xylan and mannan in the outer S2 (S2L) region of tracheids. Xylan and mannan were detected in all lignified xylem cell types (tracheids, ray tracheids, and thick-walled ray parenchyma) but were not detected in unlignified cell types (thin-walled ray parenchyma and resin canal parenchyma). Mannan was absent from the highly lignified compound middle lamella, but xylan occurred throughout the cell walls of tracheids. Using colocalization measurements, we confirmed that polysaccharides containing galactose, mannose, and xylose have consistent correlations with lignification. Low or unsubstituted xylans were localized in cell wall layers characterized by transverse cellulose microfibril orientation in both normal and compression wood tracheids. Our results support the theory that the assembly of wood cell walls, including lignification and microfibril orientation, may be mediated by changes in the amount and distribution of noncellulosic polysaccharides. PMID:22147521

Experimental investigation on aero-optics of supersonic turbulent boundary layers.

PubMed

Ding, Haolin; Yi, Shihe; Zhu, Yangzhu; He, Lin

2017-09-20

Nanoparticle-based planar laser scattering was used to measure the density distribution of the supersonic (Ma=3.0) turbulent boundary layer and the optical path difference (OPD), which is quite crucial for aero-optics study. Results were obtained using ray tracing. The influences of different layers in the boundary layer, turbulence scales, and light incident angle on aero-optics were examined, and the underlying flow physics were analyzed. The inner layer plays a dominant role, followed by the outer layer. One hundred OPD rms of the outer layer at different times satisfy the normal distribution better than that of the inner layer. Aero-optics induced by the outer layer is sensitive to the filter scale. When induced by the inner layer, it is not sensitive to the filter scale. The vortices with scales less than the Kolmogorov scale (=46.0  μm) have little influence on the aero-optics and could be ignored; the validity of the smallest optically active scale (=88.1  μm) proposed by Mani is verified, and vortices with scales less than that are ignored, resulting in a 1.62% decay of aero-optics; the filter with a width of 16-grid spacing (=182.4  μm) decreases OPD rms by 7.04%. With the increase of the angle between the wall-normal direction and the light-incident direction, the aero-optics becomes more serious, and the difference between the distribution of the OPD rms and the normal distribution increases. The difficulty of aero-optics correction is increased. Light tilted toward downstream experiences more distortions than when tilted toward upstream at the same angle relative to the wall-normal direction.

Fire frequency, area burned, and severity: A quantitative approach to defining a normal fire year

USGS Publications Warehouse

Lutz, J.A.; Key, C.H.; Kolden, C.A.; Kane, J.T.; van Wagtendonk, J.W.

2011-01-01

Fire frequency, area burned, and fire severity are important attributes of a fire regime, but few studies have quantified the interrelationships among them in evaluating a fire year. Although area burned is often used to summarize a fire season, burned area may not be well correlated with either the number or ecological effect of fires. Using the Landsat data archive, we examined all 148 wildland fires (prescribed fires and wildfires) >40 ha from 1984 through 2009 for the portion of the Sierra Nevada centered on Yosemite National Park, California, USA. We calculated mean fire frequency and mean annual area burned from a combination of field- and satellite-derived data. We used the continuous probability distribution of the differenced Normalized Burn Ratio (dNBR) values to describe fire severity. For fires >40 ha, fire frequency, annual area burned, and cumulative severity were consistent in only 13 of 26 years (50 %), but all pair-wise comparisons among these fire regime attributes were significant. Borrowing from long-established practice in climate science, we defined "fire normals" to be the 26 year means of fire frequency, annual area burned, and the area under the cumulative probability distribution of dNBR. Fire severity normals were significantly lower when they were aggregated by year compared to aggregation by area. Cumulative severity distributions for each year were best modeled with Weibull functions (all 26 years, r2 ??? 0.99; P < 0.001). Explicit modeling of the cumulative severity distributions may allow more comprehensive modeling of climate-severity and area-severity relationships. Together, the three metrics of number of fires, size of fires, and severity of fires provide land managers with a more comprehensive summary of a given fire year than any single metric.

The application of the piecewise linear approximation to the spectral neighborhood of soil line for the analysis of the quality of normalization of remote sensing materials

NASA Astrophysics Data System (ADS)

Kulyanitsa, A. L.; Rukhovich, A. D.; Rukhovich, D. D.; Koroleva, P. V.; Rukhovich, D. I.; Simakova, M. S.

2017-04-01

The concept of soil line can be to describe the temporal distribution of spectral characteristics of the bare soil surface. In this case, the soil line can be referred to as the multi-temporal soil line, or simply temporal soil line (TSL). In order to create TSL for 8000 regular lattice points for the territory of three regions of Tula oblast, we used 34 Landsat images obtained in the period from 1985 to 2014 after their certain transformation. As Landsat images are the matrices of the values of spectral brightness, this transformation is the normalization of matrices. There are several methods of normalization that move, rotate, and scale the spectral plane. In our study, we applied the method of piecewise linear approximation to the spectral neighborhood of soil line in order to assess the quality of normalization mathematically. This approach allowed us to range normalization methods according to their quality as follows: classic normalization > successive application of the turn and shift > successive application of the atmospheric correction and shift > atmospheric correction > shift > turn > raw data. The normalized data allowed us to create the maps of the distribution of a and b coefficients of the TSL. The map of b coefficient is characterized by the high correlation with the ground-truth data obtained from 1899 soil pits described during the soil surveys performed by the local institute for land management (GIPROZEM).

Distributions of Cognates in Europe as Based on Levenshtein Distance

ERIC Educational Resources Information Center

Schepens, Job; Dijkstra, Ton; Grootjen, Franc

2012-01-01

Researchers on bilingual processing can benefit from computational tools developed in artificial intelligence. We show that a normalized Levenshtein distance function can efficiently and reliably simulate bilingual orthographic similarity ratings. Orthographic similarity distributions of cognates and non-cognates were identified across pairs of…

Amyloplasts That Sediment in Protonemata of the Moss Ceratodon purpureus Are Nonrandomly Distributed in Microgravity1

PubMed Central

Kern, Volker D.; Smith, Jeffrey D.; Schwuchow, Jochen M.; Sack, Fred D.

2001-01-01

Little is known about whether or how plant cells regulate the position of heavy organelles that sediment toward gravity. Dark-grown protonemata of the moss Ceratodon purpureus displays a complex plastid zonation in that only some amyloplasts sediment along the length of the tip cell. If gravity is the major force determining the position of amyloplasts that sediment, then these plastids should be randomly distributed in space. Instead, amyloplasts were clustered in the subapical region in microgravity. Cells rotated on a clinostat on earth had a roughly similar non-random plastid distribution. Subapical clusters were also found in ground controls that were inverted and kept stationary, but the distribution profile differed considerably due to amyloplast sedimentation. These findings indicate the existence of as yet unknown endogenous forces and mechanisms that influence amyloplast position and that are normally masked in stationary cells grown on earth. It is hypothesized that a microtubule-based mechanism normally compensates for g-induced drag while still allowing for regulated amyloplast sedimentation. PMID:11299388

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

[Stress analysis of the mandible by 3D FEA in normal human being under three loading conditions].

PubMed

Sun, Jian; Zhang, Fu-qiang; Wang, Dong-wei; Yu, Jia; Wang, Cheng-tao

2004-02-01

The condition and character of stress distribution in the mandibular in normal human being during centric, protrusive, laterotrusive occlusion were analysed. The three-dimensional finite element model of the mandibular was developed by helica CT scanning and CAD/CAM software, and three-dimensional finite element stress analysis was done by ANSYS software. Three-dimensional finite element model of the mandibular was generated. Under these three occlusal conditions, the stress of various regions in the mandible were distributed unequally, and the stress feature was different;while the stress of corresponding region in bilateral mandibular was in symmetric distribution. The stress value of condyle neck, the posterior surface of coronoid process and mandibular angle were high. The material properties of mandible were closely correlated to the value of stress. Stress distribution were similar according to the three different loading patterns, but had different effects on TMJ joint. The concentrated areas of stress were in the condyle neck, the posterior surface of coronoid process and mandibular angle.

Robust Methods for Moderation Analysis with a Two-Level Regression Model.

PubMed

Yang, Miao; Yuan, Ke-Hai

2016-01-01

Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.

Evaluation of the best fit distribution for partial duration series of daily rainfall in Madinah, western Saudi Arabia

NASA Astrophysics Data System (ADS)

Alahmadi, F.; Rahman, N. A.; Abdulrazzak, M.

2014-09-01

Rainfall frequency analysis is an essential tool for the design of water related infrastructure. It can be used to predict future flood magnitudes for a given magnitude and frequency of extreme rainfall events. This study analyses the application of rainfall partial duration series (PDS) in the vast growing urban Madinah city located in the western part of Saudi Arabia. Different statistical distributions were applied (i.e. Normal, Log Normal, Extreme Value type I, Generalized Extreme Value, Pearson Type III, Log Pearson Type III) and their distribution parameters were estimated using L-moments methods. Also, different selection criteria models are applied, e.g. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC) and Anderson-Darling Criterion (ADC). The analysis indicated the advantage of Generalized Extreme Value as the best fit statistical distribution for Madinah partial duration daily rainfall series. The outcome of such an evaluation can contribute toward better design criteria for flood management, especially flood protection measures.

Distribution of transvascular pathway sizes through the pulmonary microvascular barrier.

PubMed

McNamee, J E

1987-01-01

Mathematical models of solute and water exchange in the lung have been helpful in understanding factors governing the volume flow rate and composition of pulmonary lymph. As experimental data and models become more encompassing, parameter identification becomes more difficult. Pore sizes in these models should approach and eventually become equivalent to actual physiological pathway sizes as more complex and accurate models are tried. However, pore sizes and numbers vary from model to model as new pathway sizes are added. This apparent inconsistency of pore sizes can be explained if it is assumed that the pulmonary blood-lymph barrier is widely heteroporous, for example, being composed of a continuous distribution of pathway sizes. The sieving characteristics of the pulmonary barrier are reproduced by a log normal distribution of pathway sizes (log mean = -0.20, log s.d. = 1.05). A log normal distribution of pathways in the microvascular barrier is shown to follow from a rather general assumption about the nature of the pulmonary endothelial junction.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Robustness of S1 statistic with Hodges-Lehmann for skewed distributions

NASA Astrophysics Data System (ADS)

Ahad, Nor Aishah; Yahaya, Sharipah Soaad Syed; Yin, Lee Ping

2016-10-01

Analysis of variance (ANOVA) is a common use parametric method to test the differences in means for more than two groups when the populations are normally distributed. ANOVA is highly inefficient under the influence of non- normal and heteroscedastic settings. When the assumptions are violated, researchers are looking for alternative such as Kruskal-Wallis under nonparametric or robust method. This study focused on flexible method, S1 statistic for comparing groups using median as the location estimator. S1 statistic was modified by substituting the median with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MADn to produce two different test statistics for comparing groups. Bootstrap method was used for testing the hypotheses since the sampling distributions of these modified S1 statistics are unknown. The performance of the proposed statistic in terms of Type I error was measured and compared against the original S1 statistic, ANOVA and Kruskal-Wallis. The propose procedures show improvement compared to the original statistic especially under extremely skewed distribution.

SMALL-SCALE AND GLOBAL DYNAMOS AND THE AREA AND FLUX DISTRIBUTIONS OF ACTIVE REGIONS, SUNSPOT GROUPS, AND SUNSPOTS: A MULTI-DATABASE STUDY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muñoz-Jaramillo, Andrés; Windmueller, John C.; Amouzou, Ernest C.

2015-02-10

In this work, we take advantage of 11 different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions—where a pure Weibull (log-normal) characterizesmore » the distribution of structures with fluxes below (above) 10{sup 21}Mx (10{sup 22}Mx). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended to smaller fluxes), making our results compatible with the results of Parnell et al. We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection)« less

Theory of the intermediate stage of crystal growth with applications to insulin crystallization

NASA Astrophysics Data System (ADS)

Barlow, D. A.

2017-07-01

A theory for the intermediate stage of crystal growth, where two defining equations one for population continuity and another for mass-balance, is used to study the kinetics of the supersaturation decay, the homogeneous nucleation rate, the linear growth rate and the final distribution of crystal sizes for the crystallization of bovine and porcine insulin from solution. The cited experimental reports suggest that the crystal linear growth rate is directly proportional to the square of the insulin concentration in solution for bovine insulin and to the cube of concentration for porcine. In a previous work, it was shown that the above mentioned system could be solved for the case where the growth rate is directly proportional to the normalized supersaturation. Here a more general solution is presented valid for cases where the growth rate is directly proportional to the normalized supersaturation raised to the power of any positive integer. The resulting expressions for the time dependent normalized supersaturation and crystal size distribution are compared with experimental reports for insulin crystallization. An approximation for the maximum crystal size at the end of the intermediate stage is derived. The results suggest that the largest crystal size in the distribution at the end of the intermediate stage is maximized when nucleation is restricted to be only homogeneous. Further, the largest size in the final distribution depends only weakly upon the initial supersaturation.

Body fat content, fat distribution and adipocytokine production and their correlation with fertility markers in young adult men and women conceived by intracytoplasmic sperm injection (ICSI).

PubMed

Belva, F; De Schepper, J; Roelants, M; Tournaye, H; Bonduelle, M; Provyn, S

2018-06-01

Differences in body fat content during childhood and adolescence have been described in offspring conceived by in vitro fertilisation (IVF) and intracytoplasmic sperm injection (ICSI). However, data on body fat and its distribution as well as on adipocytokine production in young adults conceived by ICSI are nonexistent. We investigated if young adult men and women conceived by ICSI have a normal body fat patterning and adipocytokine production. Cohort study. One hundred twenty-seven young adults conceived by ICSI and 138 peers born after spontaneous conception. Anthropometric parameters (skinfold thickness, hip and waist circumferences), dual X-ray absorptiometry (whole body and regional) measurements and adipocytokine levels (leptin and adiponectin) were analysed in relation to fertility markers (serum anti-Mullerian hormone (AMH) and inhibin B). While at age 18 years, a normal body fat distribution and normal leptin and adiponectin production was found in both male and female ICSI offspring, young men conceived by ICSI had a higher peripheral fat deposition in comparison with spontaneously conceived peers. No correlation between AMH and inhibin B with leptin or adiponectin was observed. While men conceived by ICSI, but not women, had a higher peripheral fat deposition, body fat distribution as well as mean levels of adipocytokines were not affected by the mode of conception. © 2018 John Wiley & Sons Ltd.

Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

PubMed

Agresti, Alan; Kateri, Maria

2017-03-01

We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals Φ(β/2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf Φ and effect β that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1+exp(β)] with the log-log link and equals approximately exp(β/2)/[1+exp(β/2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example. © 2016, The International Biometric Society.

Normal Distribution of CD8+ T-Cell-Derived ELISPOT Counts within Replicates Justifies the Reliance on Parametric Statistics for Identifying Positive Responses.

PubMed

Karulin, Alexey Y; Caspell, Richard; Dittrich, Marcus; Lehmann, Paul V

2015-03-02

Accurate assessment of positive ELISPOT responses for low frequencies of antigen-specific T-cells is controversial. In particular, it is still unknown whether ELISPOT counts within replicate wells follow a theoretical distribution function, and thus whether high power parametric statistics can be used to discriminate between positive and negative wells. We studied experimental distributions of spot counts for up to 120 replicate wells of IFN-γ production by CD8+ T-cell responding to EBV LMP2A (426 - 434) peptide in human PBMC. The cells were tested in serial dilutions covering a wide range of average spot counts per condition, from just a few to hundreds of spots per well. Statistical analysis of the data using diagnostic Q-Q plots and the Shapiro-Wilk normality test showed that in the entire dynamic range of ELISPOT spot counts within replicate wells followed a normal distribution. This result implies that the Student t-Test and ANOVA are suited to identify positive responses. We also show experimentally that borderline responses can be reliably detected by involving more replicate wells, plating higher numbers of PBMC, addition of IL-7, or a combination of these. Furthermore, we have experimentally verified that the number of replicates needed for detection of weak responses can be calculated using parametric statistics.

An asymptotic analysis of the logrank test.

PubMed

Strawderman, R L

1997-01-01

Asymptotic expansions for the null distribution of the logrank statistic and its distribution under local proportional hazards alternatives are developed in the case of iid observations. The results, which are derived from the work of Gu (1992) and Taniguchi (1992), are easy to interpret, and provide some theoretical justification for many behavioral characteristics of the logrank test that have been previously observed in simulation studies. We focus primarily upon (i) the inadequacy of the usual normal approximation under treatment group imbalance; and, (ii) the effects of treatment group imbalance on power and sample size calculations. A simple transformation of the logrank statistic is also derived based on results in Konishi (1991) and is found to substantially improve the standard normal approximation to its distribution under the null hypothesis of no survival difference when there is treatment group imbalance.

Sensitivity of the normalized difference vegetation index to subpixel canopy cover, soil albedo, and pixel scale

NASA Technical Reports Server (NTRS)

Jasinski, Michael F.

1990-01-01

An analytical framework is provided for examining the physically based behavior of the normalized difference vegetation index (NDVI) in terms of the variability in bulk subpixel landscape components and with respect to variations in pixel scales, within the context of the stochastic-geometric canopy reflectance model. Analysis focuses on regional scale variability in horizontal plant density and soil background reflectance distribution. Modeling is generalized to different plant geometries and solar angles through the use of the nondimensional solar-geometric similarity parameter. Results demonstrate that, for Poisson-distributed plants and for one deterministic distribution, NDVI increases with increasing subpixel fractional canopy amount, decreasing soil background reflectance, and increasing shadows, at least within the limitations of the geometric reflectance model. The NDVI of a pecan orchard and a juniper landscape is presented and discussed.

Ring-like spatial distribution of laser accelerated protons in the ultra-high-contrast TNSA-regime

NASA Astrophysics Data System (ADS)

Becker, G. A.; Tietze, S.; Keppler, S.; Reislöhner, J.; Bin, J. H.; Bock, L.; Brack, F.-E.; Hein, J.; Hellwing, M.; Hilz, P.; Hornung, M.; Kessler, A.; Kraft, S. D.; Kuschel, S.; Liebetrau, H.; Ma, W.; Polz, J.; Schlenvoigt, H.-P.; Schorcht, F.; Schwab, M. B.; Seidel, A.; Zeil, K.; Schramm, U.; Zepf, M.; Schreiber, J.; Rykovanov, S.; Kaluza, M. C.

2018-05-01

The spatial distribution of protons accelerated from submicron-thick plastic foil targets using multi-terawatt, frequency-doubled laser pulses with ultra-high temporal contrast has been investigated experimentally. A very stable, ring-like beam profile of the accelerated protons, oriented around the target’s normal direction has been observed. The ring’s opening angle has been found to decrease with increasing foil thicknesses. Two-dimensional particle-in-cell simulations reproduce our results indicating that the ring is formed during the expansion of the proton density distribution into the vacuum as described by the mechanism of target-normal sheath acceleration. Here—in addition to the longitudinal electric fields responsible for the forward acceleration of the protons—a lateral charge separation leads to transverse field components accelerating the protons in the lateral direction.

Electrocardiogram reference intervals for clinically normal wild-born chimpanzees (Pan troglodytes).

PubMed

Atencia, Rebeca; Revuelta, Luis; Somauroo, John D; Shave, Robert E

2015-08-01

To generate reference intervals for ECG variables in clinically normal chimpanzees (Pan troglodytes). 100 clinically normal (51 young [< 10 years old] and 49 adult [≥ 10 years old]) wild-born chimpanzees. Electrocardiograms collected between 2009 and 2013 at the Tchimpounga Chimpanzee Rehabilitation Centre were assessed to determine heart rate, PR interval, QRS duration, QT interval, QRS axis, P axis, and T axis. Electrocardiographic characteristics for left ventricular hypertrophy (LVH) and morphology of the ST segment, T wave, and QRS complex were identified. Reference intervals for young and old animals were calculated as mean ± 1.96•SD for normally distributed data and as 5th to 95th percentiles for data not normally distributed. Differences between age groups were assessed by use of unpaired Student t tests. RESULTS Reference intervals were generated for young and adult wild-born chimpanzees. Most animals had sinus rhythm with small or normal P wave morphology; 24 of 51 (47%) young chimpanzees and 30 of 49 (61%) adult chimpanzees had evidence of LVH as determined on the basis of criteria for humans. Cardiac disease has been implicated as the major cause of death in captive chimpanzees. Species-specific ECG reference intervals for chimpanzees may aid in the diagnosis and treatment of animals with, or at risk of developing, heart disease. Chimpanzees with ECG characteristics outside of these intervals should be considered for follow-up assessment and regular cardiac monitoring.

Comparative study of nonlinear properties of EEG signals of normal persons and epileptic patients

PubMed Central

2009-01-01

Background Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak et al. [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusion In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation. PMID:19619290

Simulation study of pO2 distribution in induced tumour masses and normal tissues within a microcirculation environment.

PubMed

Li, Mao; Li, Yan; Wen, Peng Paul

2014-01-01

The biological microenvironment is interrupted when tumour masses are introduced because of the strong competition for oxygen. During the period of avascular growth of tumours, capillaries that existed play a crucial role in supplying oxygen to both tumourous and healthy cells. Due to limitations of oxygen supply from capillaries, healthy cells have to compete for oxygen with tumourous cells. In this study, an improved Krogh's cylinder model which is more realistic than the previously reported assumption that oxygen is homogeneously distributed in a microenvironment, is proposed to describe the process of the oxygen diffusion from a capillary to its surrounding environment. The capillary wall permeability is also taken into account. The simulation study is conducted and the results show that when tumour masses are implanted at the upstream part of a capillary and followed by normal tissues, the whole normal tissues suffer from hypoxia. In contrast, when normal tissues are ahead of tumour masses, their pO2 is sufficient. In both situations, the pO2 in the whole normal tissues drops significantly due to the axial diffusion at the interface of normal tissues and tumourous cells. As the existence of the axial oxygen diffusion cannot supply the whole tumour masses, only these tumourous cells that are near the interface can be partially supplied, and have a small chance to survive.

[Renal excretion of total porphyrins and hippuric acid in rats].

PubMed

Gartzke, J; Burck, D

1986-09-01

The amounts of total porphyrins, hippuric acid and creatinine, excreted in urine by adult male Wistar rats, exhibited normal distributions for hippuric acid and creatinine, but a bimodal distribution for total porphyrins. This typical distribution of total porphyrins was still observed when creatinine was used as reference parameter. In biochemical and toxicological experiments in rats, the tested parameters should be therefore be investigated for homogeneity.

Characterization of the Distribution of the Lz Index of Person Fit According to the Estimated Proficiency Level

ERIC Educational Resources Information Center

Raiche, Gilles; Blais, Jean-Guy

2005-01-01

The distribution of person fit indices is not easy to describe in tests where the item sample is too small to conform to a theoretical asymptotic statistical distribution, particularly the normal N(0,1). In practice, it is always the fact and, consequently, it is difficult to get the critical percentile value indicating person misfit. First, we…

How to Introduce Historically the Normal Distribution in Engineering Education: A Classroom Experiment

ERIC Educational Resources Information Center

Blanco, Monica; Ginovart, Marta

2010-01-01

Little has been explored with regard to introducing historical aspects in the undergraduate statistics classroom in engineering studies. This article focuses on the design, implementation and assessment of a specific activity concerning the introduction of the normal probability curve and related aspects from a historical dimension. Following a…

76 FR 66660 - Special Conditions: Gulfstream Aerospace LP (GALP) Model G280 Airplane, Operation Without Normal...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-10-27

... distribution and equipment-loads-demand condition. 2. After the unrestorable loss of normal engine generator... DEPARTMENT OF TRANSPORTATION Federal Aviation Administration 14 CFR Part 25 [Docket No. FAA-2011-1172: Notice No. 25-11-17-SC] Special Conditions: Gulfstream Aerospace LP (GALP) Model G280 Airplane...

The Inverted Student Density and Test Scores.

ERIC Educational Resources Information Center

Boldt, Robert F.

The inverted density is one whose contour lines are spheroidal as in the normal distribution, but whose moments differ from those of the normal in that its conditional arrays are not homoscedastic, being quadratic functions of the values of the linear regression functions. It is also platykurtic, its measure of kurtosis ranging from that of the…

A General Approach to the Evaluation of Ventilation-Perfusion Ratios in Normal and Abnormal Lungs

ERIC Educational Resources Information Center

Wagner, Peter D.

1977-01-01

Outlines methods for manipulating multiple gas data so as to gain the greatest amount of insight into the properties of ventilation-perfusion distributions. Refers to data corresponding to normal and abnormal lungs. Uses a two-dimensional framework with the respiratory gases of oxygen and carbon dioxide. (CS)

Automated scoring system of standard uptake value for torso FDG-PET images

NASA Astrophysics Data System (ADS)

Hara, Takeshi; Kobayashi, Tatsunori; Kawai, Kazunao; Zhou, Xiangrong; Itoh, Satoshi; Katafuchi, Tetsuro; Fujita, Hiroshi

2008-03-01

The purpose of this work was to develop an automated method to calculate the score of SUV for torso region on FDG-PET scans. The three dimensional distributions for the mean and the standard deviation values of SUV were stored in each volume to score the SUV in corresponding pixel position within unknown scans. The modeling methods is based on SPM approach using correction technique of Euler characteristic and Resel (Resolution element). We employed 197 nor-mal cases (male: 143, female: 54) to assemble the normal metabolism distribution of FDG. The physique were registered each other in a rectangular parallelepiped shape using affine transformation and Thin-Plate-Spline technique. The regions of the three organs were determined based on semi-automated procedure. Seventy-three abnormal spots were used to estimate the effectiveness of the scoring methods. As a result, the score images correctly represented that the scores for normal cases were between zeros to plus/minus 2 SD. Most of the scores of abnormal spots associated with cancer were lager than the upper of the SUV interval of normal organs.

Body fat distribution of overweight females with a history of weight cycling.

PubMed

Wallner, S J; Luschnigg, N; Schnedl, W J; Lahousen, T; Sudi, K; Crailsheim, K; Möller, R; Tafeit, E; Horejsi, R

2004-09-01

Weight cycling may cause a redistribution of body fat to the upper body fat compartments. We investigated the distribution of subcutaneous adipose tissue (SAT) in 30 overweight women with a history of weight-cycling and age-matched controls (167 normal weight and 97 overweight subjects). Measurements of SAT were performed using an optical device, the Lipometer. The SAT topography describes the thicknesses of SAT layers at 15 anatomically well-defined body sites from neck to calf. The overweight women with a history of weight cycling had significantly thicker SAT layers on the upper body compared to the overweight controls, but even thinner SAT layers on their legs than the normal weight women. An android fat pattern was attributed to overweight females and, even more pronounced, to the weight cyclers. The majority of normal weight women showed a gynoid fat pattern. Using stepwise discriminant analysis, 89.0% of all weight cyclers and overweight controls could be classified correctly into the two groups. These findings show the importance of normal weight maintenance as a health-promoting factor.

Higher incidence of small Y chromosome in humans with trisomy 21 (Down syndrome).

PubMed

Verma, R S; Huq, A; Madahar, C; Qazi, Q; Dosik, H

1982-09-01

The length of the Y chromosome was measured in 42 black patients with trisomy 21 (47,XY,+21) and a similar number of normal individuals of American black ancestry. The length of the Y was expressed as a function of Y/F ratio and arbitrarily classified into five groups using subjectively defined criteria as follows: very small, small, average, large, and very large. Thirty-eight % of the trisomy 21 patients had small or very small Ys compared to 2.38% of the controls (P less than 0.01). In both populations the size of the Y was not normally distributed. In the normals it was skewed to the left, whereas in the Downs the distribution was flat (platykurtic). A significantly higher incidence of Y length heteromorphisms was noted in the Down as compared to the normal black population. In the light of our current understanding that about one-third of all trisomy 21 patients are due to paternal nondisjunction, it may be tempting to speculate that males with small Y are at an increased risk for nondisjunction of the 21 chromosome.

Theoretical Calculation of the Electron Transport Parameters and Energy Distribution Function for CF3I with noble gases mixtures using Monte Carlo simulation program

NASA Astrophysics Data System (ADS)

Jawad, Enas A.

2018-05-01

In this paper, The Monte Carlo simulation program has been used to calculation the electron energy distribution function (EEDF) and electric transport parameters for the gas mixtures of The trif leoroiodo methane (CF3I) ‘environment friendly’ with a noble gases (Argon, Helium, kryptos, Neon and Xenon). The electron transport parameters are assessed in the range of E/N (E is the electric field and N is the gas number density of background gas molecules) between 100 to 2000Td (1 Townsend = 10-17 V cm2) at room temperature. These parameters, namely are electron mean energy (ε), the density –normalized longitudinal diffusion coefficient (NDL) and the density –normalized mobility (μN). In contrast, the impact of CF3I in the noble gases mixture is strongly apparent in the values for the electron mean energy, the density –normalized longitudinal diffusion coefficient and the density –normalized mobility. Note in the results of the calculation agreed well with the experimental results.

In vivo NMR imaging of sodium-23 in the human head.

PubMed

Hilal, S K; Maudsley, A A; Ra, J B; Simon, H E; Roschmann, P; Wittekoek, S; Cho, Z H; Mun, S K

1985-01-01

We report the first clinical nuclear magnetic resonance (NMR) images of cerebral sodium distribution in normal volunteers and in patients with a variety of pathological lesions. We have used a 1.5 T NMR magnet system. When compared with proton distribution, sodium shows a greater variation in its concentration from tissue to tissue and from normal to pathological conditions. Image contrast calculated on the basis of sodium concentration is 7 to 18 times greater than that of proton spin density. Normal images emphasize the extracellular compartments. In the clinical studies, areas of recent or old cerebral infarction and tumors show a pronounced increase of sodium content (300-400%). Actual measurements of image density values indicate that there is probably a further accentuation of the contrast by the increased "NMR visibility" of sodium in infarcted tissue. Sodium imaging may prove to be a more sensitive means for early detection of some brain disorders than other imaging methods.

Modeling the brain morphology distribution in the general aging population

NASA Astrophysics Data System (ADS)

Huizinga, W.; Poot, D. H. J.; Roshchupkin, G.; Bron, E. E.; Ikram, M. A.; Vernooij, M. W.; Rueckert, D.; Niessen, W. J.; Klein, S.

2016-03-01

Both normal aging and neurodegenerative diseases such as Alzheimer's disease cause morphological changes of the brain. To better distinguish between normal and abnormal cases, it is necessary to model changes in brain morphology owing to normal aging. To this end, we developed a method for analyzing and visualizing these changes for the entire brain morphology distribution in the general aging population. The method is applied to 1000 subjects from a large population imaging study in the elderly, from which 900 were used to train the model and 100 were used for testing. The results of the 100 test subjects show that the model generalizes to subjects outside the model population. Smooth percentile curves showing the brain morphology changes as a function of age and spatiotemporal atlases derived from the model population are publicly available via an interactive web application at agingbrain.bigr.nl.

Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

NASA Astrophysics Data System (ADS)

Yamazaki, Dai G.; Ichiki, Kiyotomo; Takahashi, Keitaro

2011-12-01

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at k≃10-2.5Mpc-1 with the upper limit B≲3nG.

Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean.

PubMed

Krishnamoorthy, K; Oral, Evrim

2017-12-01

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples.

Positive phase space distributions and uncertainty relations

NASA Technical Reports Server (NTRS)

Kruger, Jan

1993-01-01

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Population Synthesis of Radio and Y-ray Normal, Isolated Pulsars Using Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Billman, Caleb; Gonthier, P. L.; Harding, A. K.

2013-04-01

We present preliminary results of a population statistics study of normal pulsars (NP) from the Galactic disk using Markov Chain Monte Carlo techniques optimized according to two different methods. The first method compares the detected and simulated cumulative distributions of series of pulsar characteristics, varying the model parameters to maximize the overall agreement. The advantage of this method is that the distributions do not have to be binned. The other method varies the model parameters to maximize the log of the maximum likelihood obtained from the comparisons of four-two dimensional distributions of radio and γ-ray pulsar characteristics. The advantage of this method is that it provides a confidence region of the model parameter space. The computer code simulates neutron stars at birth using Monte Carlo procedures and evolves them to the present assuming initial spatial, kick velocity, magnetic field, and period distributions. Pulsars are spun down to the present and given radio and γ-ray emission characteristics, implementing an empirical γ-ray luminosity model. A comparison group of radio NPs detected in ten-radio surveys is used to normalize the simulation, adjusting the model radio luminosity to match a birth rate. We include the Fermi pulsars in the forthcoming second pulsar catalog. We present preliminary results comparing the simulated and detected distributions of radio and γ-ray NPs along with a confidence region in the parameter space of the assumed models. We express our gratitude for the generous support of the National Science Foundation (REU and RUI), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program.