Statistics and Probability Commons^™

A Monte Carlo Power Analysis Of Traditional Repeated Measures And Hierarchical Multivariate Linear Models In Longitudinal Data Analysis, Hua Fang, Gordon P. Brooks, Maria L. Rizzo, Kimberly A. Espy, Robert S. Barcikowski

Developmental Cognitive Neuroscience Laboratory: Faculty Publications

The power properties of traditional repeated measures and hierarchical linear models have not been clearly determined in the balanced design for longitudinal studies in the current literature. A Monte Carlo power analysis of traditional repeated measures and hierarchical multivariate linear models are presented under three variance-covariance structures. Results suggest that traditional repeated measures have higher power than hierarchical linear models for main effects, but lower power for interaction effects. Significant power differences are also exhibited when power is compared across different covariance structures. Results also supplement more comprehensive empirical indexes for estimating model precision via bootstrap estimates and the approximate …

Evaluation Of Serotonin As A Feedback Inhibitor Of Lactation In The Bovine, L. L. Hernandez, C. M. Stiening, J. B. Wheelock, L. H. Baumgard, Anne M. Parkhurst, R. J. Collier

Department of Statistics: Faculty Publications

Serotonin (5-HT), a neurotransmitter synthesized from tryptophan, has been proposed as a feedback inhibitor of lactation. We determined that the gene coding for tryptophan hydroxylase 1, the rate-limiting enzyme for 5-HT synthesis, is expressed in bovine mammary epithelial cells in vitro and is upregulated by prolactin. In addition, 5-HT reduced the expression of α-lactalbumin and casein genes in vitro. Furthermore, inhibiting 5-HT synthesis with p-chlorophenylalanine or blocking the 5-HT receptor with methysergide (METH) increased milk protein gene expression. We then evaluated effects of intramammary 5-HT or METH infusion on production and milk composition in 6 multiparous Holstein cows. Cows …

J. K. Ghosh’S Contribution To Statistics: A Brief Outline, Bertrand Clarke, Subhashis Ghosal

Department of Statistics: Faculty Publications

Professor Jayanta Kumar Ghosh has contributed massively to various areas of Statistics over the last five decades. Here, we survey some of his most important contributions. In roughly chronological order, we discuss his major results in the areas of sequential analysis, foundations, asymptotics, and Bayesian inference. It is seen that he progressed from thinking about data points, to thinking about data summarization, to the limiting cases of data summarization in as they relate to parameter estimation, and then to more general aspects of modeling including prior and model selection.

An Ensemble Approach To Improved Prediction From Multitype Data, Jennifer Clarke

Department of Statistics: Faculty Publications

We have developed a strategy for the analysis of newly available binary data to improve outcome predictions based on existing data (binary or non-binary). Our strategy involves two modeling approaches for the newly available data, one combining binary covariate selection via LASSO with logistic regression and one based on logic trees. The results of these models are then compared to the results of a model based on existing data with the objective of combining model results to achieve the most accurate predictions. The combination of model predictions is aided by the use of support vector machines to identify subspaces of …

A Bayesian Test For Excess Zeros In A Zero-Inflated Power Series Distribution, Archan Bhattacharya, Bertrand S. Clarke, Gauri S. Datta

Department of Statistics: Faculty Publications

Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate distribution at zero, with a mixing probability p for the degenerate distribution. This distribution is useful for modeling count data that may have extra zeros. One question is whether the mixture model can be reduced to the power series portion, corresponding to p = 0, or whether there are so many zeros in the data that zero inflation relative to the pure power series distribution must be …

An Improved String Composition Method For Sequence Comparison, Guoqing Lu, Shunpu Zhang, Xiang Fang

Department of Statistics: Faculty Publications

Background: Historically, two categories of computational algorithms (alignment-based and alignment-free) have been applied to sequence comparison–one of the most fundamental issues in bioinformatics. Multiple sequence alignment, although dominantly used by biologists, possesses both fundamental as well as computational limitations. Consequently, alignment-free methods have been explored as important alternatives in estimating sequence similarity. Of the alignment-free methods, the string composition vector (CV) methods, which use the frequencies of nucleotide or amino acid strings to represent sequence information, show promising results in genome sequence comparison of prokaryotes. The existing CV-based methods, however, suffer certain statistical problems, thereby underestimating the amount of evolutionary …

Why Divide By (N-1) For Sample Standard Deviation?, Paul Savory

Department of Industrial and Management Systems Engineering: Instructional Materials

In statistics, the sample standard deviation is a widely used measure of the variability or dispersion of a data set. The standard deviation of a data set is the square root of its variance. In calculating the sample standard deviation, the divisor is the number of samples in the data set minus one (n-1) rather than n. This often confuses students. This paper offers a quick overview of why the divisor is (n-1) for calculating the sample standard deviation.

How Do You Interpret A Confidence Interval?, Paul Savory

Department of Industrial and Management Systems Engineering: Instructional Materials

A confidence interval (CI) is an interval estimate of a population parameter. Instead of estimating the parameter by a single value, a point estimate, an interval likely to cover the parameter is developed. Many student incorrectly interpret the meaning of a confidence interval. This paper offers a quick overview of how to correctly interpret a confidence interval.

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

Changing The Support Of A Spatial Covariate: A Simulation Study, Tisha L. Hooks, Jeffrey F. Pedersen, David B. Marx, Roch E. Gaussoin

Department of Statistics: Faculty Publications

Researchers are increasingly able to capture spatially referenced data on both a response and a covariate more frequently and in more detail. A combination of geostatisical models and analysis of covariance methods may be used to analyze such data. However, very basic questions regarding the effects of using a covariate whose support differs from that of the response variable must be addressed to utilize these methods most efficiently. In this experiment, a simulation study was conducted to assess the following: (i) the gain in efficiency when geostatistical models are used, (ii) the gain in efficiency when analysis of covariance methods …

Comments On “On The Distribution Of The Product Of Independent Rayleigh Random Variables”, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

It is pointed out that the result in Salo et al. “The Distribution of the Product of Independent Rayleigh Random Variables” IEEE Trans. Antennas Propag., vol. 54, pp. 639–643, Feb. 2006, is a particular case of a much more general result known since the 1970s. A general technique (known as the H function technique) is described that can be used derive a wide range of results similar to Salo et al.

Comments On “On The Distribution Of The Product Of Independent Rayleigh Random Variables”, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

It is pointed out that the result in Salo et al. “The Distribution of the Product of Independent Rayleigh Random Variables” IEEE Trans. Antennas Propag., vol. 54, pp. 639–643, Feb. 2006, is a particular case of a much more general result known since the 1970s. A general technique (known as the function technique) is described that can be used derive a wide range of results similar to Salo et al.

The Exact Distribution Of The Multilook Magnitude, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

Gierull provides a statistical analysis of multilook synthetic aperture radar interferograms. Various expressions for the probability density function, cumulative distribution function, and the moments of associated statistics are derived. It appears, however, that most of these expressions are based on some approximation. In this letter, the corresponding expressions are derived in their exact form, including some elementary representations for certain expressions given by Gierull. A numerical comparison of the exact and approximate expressions is provided.

On The Η - Κ Distribution, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

The recent paper by Yacoub et al. [1] introduces what is referred to as the η – κ distribution to describe the statistical variation of the envelope in a fast fading environment. The paper discusses several properties of the distribution. Two of the properties discussed are the nth moment, E(Pⁿ), and the cumulative probability function (cpf), FP_P (•), where P is a random variable representing the normalized envelope. The expression given for E(Pⁿ) (see equation (10) in Yacoub et al. [1]) is a doubly infinite sum of the Gauss hypergeometric function …

On The Η – Κ Distribution, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

The recent paper byYacoub et al. [1] introduces what is referred to as the η – κ distribution to describe the statistical variation of the envelope in a fast fading environment. The paper discusses several properties of the distribution. Two of the properties discussed are the nth moment, E(Pⁿ), and the cumulative probability function (cpf), F_P (•), where P is a random variable representing the normalized envelope. The expression given for E(Pⁿ) (see equation (10) in Yacoub et al. [1]) is a doubly infinite sum of the Gauss hypergeometric function (which, itself, is an infinite …

Variation In The U.S. Photoperiod Insensitive Sorghum Collection For Chemical And Nutritional Traits, Tisha L. Hooks, Jeffrey F. Pedersen, D. B. Marx, K. P. Vogel

Department of Statistics: Faculty Publications

Screening germplasm for chemical and nutritional content can be expensive and time consuming. Near infrared spectroscopy (NIRS) and application of geostatistical models can make screening more efficient. The objectives of this study were to utilize these technologies to: (i) generate chemical and nutritional values for the U.S. photoperiod insensitive sorghum collection, (ii) describe variability for those traits, (iii) identify accessions in the highest and lowest 1% for each trait, and (iv) describe relationships among the accessions. Accessions were grown at Ithaca, NE, during 2001 and 2002. Samples of grain were scanned and NIRS equations developed for starch, fat, crude protein, …

Trans-10, Cis-12 Conjugated Linoleic Acid Causes Inflammation And Delipidation Of White Adipose Tissue In Mice: A Microarray And Histological Analysis, P. Christopher Larosa, Jess L. Miner, Yuannan Xia, You Zhou, Stephen D. Kachman, Michael Fromm

Department of Statistics: Faculty Publications

A combined histological and microarray analysis of the white adipose tissue (WAT) of mice fed trans-10, cis-12 conjugated linoleic acid (t10c12 CLA) was performed to better define functional responses. Mice fed t10c12 CLA for 14 days lost 85% of WAT mass, 95% of adipocyte lipid droplet volume, and 15 or 47% of the number of adipocytes and total cells, respectively. Microarray profiling of replicated pools (n = 2 per day x diet) of control and treated mice (n = 140) at seven time points after 1–17 days of t10c12 CLA feeding found between 2,682 and 4,216 …

Pregnancy Rate And First-Service Conception Rate In Angus Heifers, J. Minick Bormann, L. R. Totir, Stephen D. Kachman, R. L. Fernando, D. E. Wilson

Department of Statistics: Faculty Publications

The objective of this project was to determine the genetic control of conception rate, or pregnancy percentage in Angus beef heifers. Producers from 6 herds in 5 states provided 3,144 heifer records that included breeding dates, breeding contemporary groups, service sires, and pregnancy check information. Two hundred fourteen sires of the heifers were represented; with 104 sires having less than 5 progeny, and 14 sires having greater than 50 progeny. These data were combined with performance and pedigree information, including actual and adjusted birth weights, weaning weights, and yearling weights, from the American Angus Association database. Heifer pregnancy rate varied …

Closed Form Expressions For Bayesian Sample Size, Bertrand S. Clarke, A. Yuan

Department of Statistics: Faculty Publications

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the expected value, under a fixed parameter, for certain types of functionals of the posterior density in a Bayesian analysis. The generality of our …

Reliability For Some Bivariate Exponential Distributions, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y). The algebraic form for R = Pr(X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when (X,Y) follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution is bivariate …

Quotient Of Laplace And Gumbel Random Variables, Saralees Nadarajah

Department of Statistics: Faculty Publications

The Gumbel and the Laplace distributions are perhaps two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient |X/Y| is derived when X and Y are independent Gumbel and Laplace random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.

Computation Of A Face Attractiveness Index Based On Neoclassical Canons, Symmetry, And Golden Ratios, Kendra Schmid, David Marx, Ashok Samal

Department of Statistics: Faculty Publications

Analysis of attractiveness of faces has long been a topic of research. Literature has identified many different factors that can be related to attractiveness including symmetry, averageness, sexual dimorphism and adherence to the Golden Ratio. In this research we systematically analyze the role of three factors: symmetry, conformance to Neoclassical Canons and the Golden Ratio in the determination of attractiveness of a face. Unlike many researchers, we focus on the geometry of a face and use actual faces in standardized databases for our analysis. Our results are in agreement with the literature in that males and females generally agree on …

Multivariate Analysis Of Ecologicai Data Using Canco, Anne M. Parkhurst

Department of Statistics: Faculty Publications

This book is about understanding and applying multivariate statistical methods useful for analyzing complex ecological problems. Researchers and students seeking to improve their ability to collect and analyze data from field observations and experiments, especially those interested in the response or variation of biotic communities to environmental conditions or experimental manipulation, will find this handbook helpful. The methods discussed are widely used in plant community ecology, as well as other areas in biology.

The book is tutorial in nature. The authors provide advice on how to best apply the multivariate statistical methods using the CANOCO for Windows, a licensed computer …

Effects Of Supplementation Of Whole Corn Germ On Reproductive Performance, Calf Performance, And Leptin Concentration In Primiparous And Mature Beef Cows, J. L. Martin, Richard J. Rasby, Dennis R. Brink, R. U. Lindquist, D. H. Keisler, Stephen D. Kachman

Department of Statistics: Faculty Publications

A 2-yr study using primiparous and multiparous, spring-calving, crossbred beef cows was conducted to evaluate the effects of supplemental whole corn germ on reproductive performance, calf performance, and serum leptin concentrations. Each year, cows were blocked by age and BCS and assigned randomly to one of three treatments: PRE (n = 115) cows received 1.14 kg/d (DM basis) of whole corn germ for approximately 45 d before calving; POST (n = 109) cows were fed 1.14 kg/d of whole corn germ for approximately 45 d after calving; and control cows (n = 118) were fed similar energy and protein from …

On The Linear Combination Of Exponential And Gamma Random Variables, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

The exact distribution of the linear combination αX + βY is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science.

Reliability For Some Bivariate Gamma Distributions, Saralees Nadarajah

Department of Statistics: Faculty Publications

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y). The algebraic form for R = Pr(X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X,Y) follows a bivariate distribution with dependence between X and Y. In particular, we derive explicit expressions for R when the joint distribution is …

On The Product And Ratio Of Laplace And Bessel Random Variables, Sarlees Nadarajah

Department of Statistics: Faculty Publications

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are Laplace and Bessel function random variables distributed independently of each other.

On The Product And Ratio Of Laplace And Bessel Random Variables, Saralees Nadarajah

Department of Statistics: Faculty Publications

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are Laplace and Bessel function random variables distributed independently of each other.

On The Product And Ratio Of Bessel Random Variables, Saralees Nadarajah, Arjun K. Gupta

Department of Statistics: Faculty Publications

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.

A Generalized Logistic Distribution, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

A generalized logistic distribution is proposed, based on the fact that the difference of two independent Gumbel-distributed randomvariables has the standard logistic distribution.