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The Beta Maxwell Distribution, Grace Ebunoluwa Amusan Jan 2010

The Beta Maxwell Distribution, Grace Ebunoluwa Amusan

Theses, Dissertations and Capstones

In this work we considered a general class of distributions gener- ated from the logit of the beta random variable. We looked at various works that have been done and discussed some of the results that were obtained. Special cases of this class include the beta-normal distribution, the beta-exponential distribution, the beta-Gumbell distribution, the beta-Weibull distribution, the beta-Pareto distribution and the beta-Rayleigh distribution. We looked at the probability distribution functions of each of these distributions and also look at some of their properties. Another special case of this family, a three-parameter beta-Maxwell distribution was dened and studied. Various properties of …

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Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth Jan 2010

Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth

Mathematics Faculty Publications

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.

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Principal Component Analysis And Biochemical Characterization Of Protein And Starch Reveal Primary Targets For Improving Sorghum Grain, Joshua H. Wong, D. B. Marx, Jeff D. Wilson, Bob B. Buchanan, Peggy G. Lemaux, Jeffrey F. Pedersen Jan 2010

Principal Component Analysis And Biochemical Characterization Of Protein And Starch Reveal Primary Targets For Improving Sorghum Grain, Joshua H. Wong, D. B. Marx, Jeff D. Wilson, Bob B. Buchanan, Peggy G. Lemaux, Jeffrey F. Pedersen

Department of Statistics: Faculty Publications

Limited progress has been made on genetic improvement of the digestibility of sorghum grain because of variability among different varieties. In this study, we applied multiple techniques to assess digestibility of grain from 18 sorghum lines to identify major components responsible for variability. We also identified storage proteins and enzymes as potential targets for genetic modification to improve digestibility. Results from principal component analysis revealed that content of amylose and total starch, together with protein digestibility (PD), accounted for 94% of variation in digestibility. Control of amylose content is understood and manageable. Up-regulation of genes associated with starch accumulation is …

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Reference Priors For Exponential Families With Increasing Dimension, Bertrand S. Clarke, Subhashis Ghosal Jan 2010

Reference Priors For Exponential Families With Increasing Dimension, Bertrand S. Clarke, Subhashis Ghosal

Department of Statistics: Faculty Publications

In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual information valid when p = pn increases at a sufficiently slow rate. The second term in the asymptotic expansion is the largest term that depends on the prior and can be optimized to give Jeffreys’ prior as the reference prior in …

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Desiderata For A Predictive Theory Of Statistics, Bertrand Clarke Jan 2010

Desiderata For A Predictive Theory Of Statistics, Bertrand Clarke

Department of Statistics: Faculty Publications

In many contexts the predictive validation of models or their associated prediction strategies is of greater importance than model identification which may be practically impossible. This is particularly so in fields involving complex or high dimensional data where model selection, or more generally predictor selection is the main focus of effort. This paper suggests a unified treatment for predictive analyses based on six 'desiderata'. These desiderata are an effort to clarify what criteria a good predictive theory of statistics should satisfy.

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Mathematical Themes In Economics, Machine Learning, And Bioinformatics, Matt Bogard Jan 2010

Mathematical Themes In Economics, Machine Learning, And Bioinformatics, Matt Bogard

Economics Faculty Publications

Graduate students in economics are often introduced to some very useful mathematical tools that many outside the discipline may not associate with training in economics. This essay looks at some of these tools and concepts, including constrained optimization, separating hyperplanes, supporting hyperplanes, and ‘duality.’ Applications of these tools are explored including topics from machine learning and bioinformatics.

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Sustainable Agriculture Bibliography, Matt Bogard Jan 2010

Sustainable Agriculture Bibliography, Matt Bogard

Agriculture Department Seminar Series

An annotated bibliography related to the sustainability of biotechnology and pharmaceutical technologies used in modern agriculture.

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Item Order Effects On Attitude Measures, Pei-Hua Chen Jan 2010

Item Order Effects On Attitude Measures, Pei-Hua Chen

Electronic Theses and Dissertations

The purpose of this dissertation was to examine the effects of altered item order on attitude measures for both computerized adaptive and conventional survey formats. Based on items modified from a dissertation/thesis completion survey (Green & Kluever, 1997) with three scales, three survey versions were generated with items ordered by difficulty as hard-to-easy (H-E), easy-to-hard (E-H), and five medium trait level items presented first followed by randomly ordered items (M-R) for conventional survey format. Significant differences in item difficulty and item discrimination were found for two of the three scales. Differences in scale reliability were detected for the procrastination and …

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Using R, Matt Bogard Jan 2010

Using R, Matt Bogard

Economics Faculty Publications

R is a statistical programming language with a command line interface that is becoming more and more popular every day. I have used R for data visualization, data mining/machine learning, as well as social network analysis. Initially embraced largely in academia, R is becoming the software of choice in various corporate settings.

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Using Twitter To Demonstrate Basic Concepts From Network Analysis, Matt Bogard Jan 2010

Using Twitter To Demonstrate Basic Concepts From Network Analysis, Matt Bogard

Economics Faculty Publications

Social network analysis focuses on finding patterns in interactions between people or entities. These patterns may be described in the form of a network. Network analysis in general has many applications including models of student integration and persistence, business to business supply chains, terrorist cells, or analysis of social media such as Facebook and Twitter. This presentation provides a reference for basic concepts from social network analysis with examples using tweets from Twitter.

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Noncompliance With Public Health Service (Phs) Policy On Humane Care And Use Of Laboratory Animals: An Exploratory Analysis, Leah M. Gomez, Kathleen Conlee, Martin Stephens Jan 2010

Noncompliance With Public Health Service (Phs) Policy On Humane Care And Use Of Laboratory Animals: An Exploratory Analysis, Leah M. Gomez, Kathleen Conlee, Martin Stephens

Laboratory Experiments Collection

The National Institutes of Health (NIH) is a major biomedical research-funding body in the United States. Approximately 40% of NIH-funded research involves experimentation on nonhuman animals (Monastersky, 2008). Institutions that conduct animal research with NIH funds must adhere to the Public Health Service (PHS) care and use standards of the Office of Laboratory Animal Welfare (OLAW, 2002a). Institutions deviating significantly from the PHS’s animal care and use standards must report these incidents to the NIH’s OLAW. This study is an exploratory analysis of all the significant deviations reported by animal-research facilities to OLAW during a 3-month period. The study identifies …

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Gronwall-Ouiang-Type Integral Inequalities On Time Scales, Ailian Liu, Martin Bohner Jan 2010

Gronwall-Ouiang-Type Integral Inequalities On Time Scales, Ailian Liu, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We present several Gronwall-OuIang-type integral inequalities on time scales. Firstly, an OuIang inequality on time scales is discussed. Then we extend the Gronwall-type inequalities to multiple integrals. Some special cases of our results contain continuous Gronwall-type inequalities and their discrete analogues. Several examples are included to illustrate our results at the end.

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Weyl-Titchmarsh Theory For Hamiltonian Dynamic Systems, Shurong Sun, Shaozhu Chen, Martin Bohner Jan 2010

Weyl-Titchmarsh Theory For Hamiltonian Dynamic Systems, Shurong Sun, Shaozhu Chen, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale T , which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for T= ℝ and T= ℤ within one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i) M(λ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for …

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Ua56/1 Fact Book, Wku Institutional Research Jan 2010

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

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Is Screening Cargo Containers For Smuggled Nuclear Threats Worthwhile?, Jason R. W. Merrick, Laura A. Mclay Jan 2010

Is Screening Cargo Containers For Smuggled Nuclear Threats Worthwhile?, Jason R. W. Merrick, Laura A. Mclay

Statistical Sciences and Operations Research Publications

In recent years, Customs and Border Protection (CBP) has installed radiation sensors to screen cargo containers entering theUnited States. They are concerned that terrorists could use containers to smuggle radiological material into the country and carry out attacks with dirty bombs or a nuclear device. Recent studies have questioned the value of improving this screening system with new sensor technology. The cost of delays caused by frequent false alarms outweighs any reduction in the probability of an attack in an expected cost analysis. We extend existing methodology in three ways to demonstrate how additional factors affect the value of screening …

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Type Ii Robustness Of The Null Hypothesis Rho = 0 For Non-Normal Distributions, Stephanie Wren Jan 2010

Type Ii Robustness Of The Null Hypothesis Rho = 0 For Non-Normal Distributions, Stephanie Wren

Wayne State University Dissertations

Is the t test statistic for the Pearson Product Moment Correlation Coefficient robust to errors of the second kind? This investigation indirectly measured the effects of power through a type 2 error rate robustness study. The results were revealing.

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Identification Of Neuroblastoma And Its Prognostic Markers Using Raman Spectroscopy, Rachel Kast Jan 2010

Identification Of Neuroblastoma And Its Prognostic Markers Using Raman Spectroscopy, Rachel Kast

Wayne State University Dissertations

Introduction: Neuroblastoma is the most common cancer of infancy. It is one of several peripheral nervous system tumors, including ganglioneuroma, peripheral nerve sheath tumor, and pheochromocytoma. It is commonly situated on the adrenal gland. It displays similar histology to other small round blue cell tumors, including non-Hodgkin lymphoma, rhabdomyosarcoma, and Ewing sarcoma. One method of judging neuroblastoma aggressiveness uses tumor histology factors, including mitosis-karyorrhexis index, Schwannian stromal development, degree of differentiation, and patient age. Tumor aggressiveness can also be judged based on the amplification of certain genes, including MYCN. Raman spectroscopy is a physics-based method which identifies the biochemical …

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Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li Jan 2010

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

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Simulating Power For One-Way Anova By Using Non-Normal Error Distributions, Caixia Xu Jan 2010

Simulating Power For One-Way Anova By Using Non-Normal Error Distributions, Caixia Xu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Usually we assume that the distribution of the additive errors in a one-way ANOVA linear model is normal. However, exceptions to this assumption about the error distribution may exist. In such cases, we might consider non-normal error distributions, but proceed with the "usual" ANOVA F-test analyses. This study focuses on simulating power for one-way ANOVA when using non-normal error distributions.

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Bayesian Nonparametric Regression With A Flexible Error Term Distribution, Courtney Marie Barnes Jan 2010

Bayesian Nonparametric Regression With A Flexible Error Term Distribution, Courtney Marie Barnes

Open Access Theses & Dissertations

Datasets often exhibit heavy tailed behavior and standard analyses are often heavily influenced by outliers. We propose a nonparametric regression model whose error term distribution is a mixture of a normal and a Student t distribution. This results in a model that is more resistant to outliers compared to a model with a normal error term.

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Identifying Influential Observations Through The Intraclass Correlation Coefficient, Angel De Jesus Davalos Jan 2010

Identifying Influential Observations Through The Intraclass Correlation Coefficient, Angel De Jesus Davalos

Open Access Theses & Dissertations

In this thesis, we analyze the performance of adapting the DFBETA statistic for identifying influential observations on the intraclass correlation coefficient under the assumptions of the one-way random effects model. Additionally, we introduce an approach for transforming negative intraclass correlation coefficient estimation values using the method of moments estimator. We apply this method on a data set of repeated blood pressure measurements, after which we will investigate implications of identifying influential observations.

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Detecting Outliers And Influential Observations In Survival Model., Nor Akmal Md Noh Jan 2010

Detecting Outliers And Influential Observations In Survival Model., Nor Akmal Md Noh

Student Works (2010-2019)

This study proposes outlier and influential observation detection procedures for Cox proportional hazard model. In the estimation process, the parameters for Cox proportional hazard model are estimated using partial likelihood method, while the baseline hazard estimates are obtained using Nelson-Aalen method. The procedure of outlier detection is based on three types of residuals; deviance, log-odd and normal deviate residuals. We study their properties and compare their performance in detecting outliers via simulation. On the other hand, we propose a procedure of identifying influential observation using forward search method. The method has been shown to be effective in detecting influential observations …

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Statistical Modelling And Inference For A Class Of Bivariate And Related Distributions., Ng Choung Min Jan 2010

Statistical Modelling And Inference For A Class Of Bivariate And Related Distributions., Ng Choung Min

Student Works (2010-2019)

This thesis considers bivariate extension of the Meixner class of distributions by the method of generalized trivariate reduction so that the marginal distributions have different parameters; in particular, a new bivariate negative binomial (BNB) distribution is examined. Different marginal parameters allow flexibility in statistical modelling and simulation studies when different marginal distributions and a specified correlation are required. The multivariate extension of this class of distributions is also given. Specifically, various interesting properties of the proposed BNB distribution, such as canonical expansion and quadrant dependence are examined. In addition, potential applications of the proposed distribution, as a bivariate mixed Poisson …

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Some Problems Of Outliers In Circular Data., Ali H.M. Abuzaid Jan 2010

Some Problems Of Outliers In Circular Data., Ali H.M. Abuzaid

Student Works (2010-2019)

This study considers three problems of outliers in circular statistics. The first problem is an attempt to use the standard outlier detection procedures for linear data set by approximating circular variables by linear variables. This is possible for large values of concentration parameter. Series of simulation studies are carried out to specify the accepted value of the concentration parameter so that the von Mises distribution can be approximated by normal distribution. The second is the problem of outliers in circular samples. Two numerical tests of discordancy are proposed to identify outliers. The test statistics are based on the summation of …

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Anomalous Diffusion In Trading Models., Sidiq Mohamad Khidzir Jan 2010

Anomalous Diffusion In Trading Models., Sidiq Mohamad Khidzir

Student Works (2010-2019)

Econophysics is an interdisciplinary research field applying the mathematical methods of statistical physics to economics and finance. It emphasizes quantitative analysis of large amounts of economic and financial data as oppose to the more philosophical approach of political economics. A popular topic studied in econophysics is the distribution of wealth.Many models have been proposed to explain the trading dynamics [12,13] leading to the distribution of wealth universally observed in many countries. A more recent topic in econophysics is the movement of money studied by Brockmann in [19,20]. In this work, we are interested in studying the relation between the distribution …

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Mixture Model Clustering For Very Large Data Sets., Leong Siow Hoo Jan 2010

Mixture Model Clustering For Very Large Data Sets., Leong Siow Hoo

Student Works (2010-2019)

This thesis develops mixture model clustering algorithms scalable to data sets that do not fit into the computer memory buffer. Two algorithms, FlexClust and FlexClustMix, are proposed for clustering very large continuous and mixed data sets respectively. The basic framework of the algorithms is to scale down data incrementally using data compression, and incorporates the later compressed data into the current model with the ability to recover new clusters that have been missed out in the earlier compressed data. It consists of three modules: 1) incremental compression, 2) detecting change in cluster structure, and 3) update of current model. In …

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Confidence Intervals In Survival Analysis, Tan Shay Kee Jan 2010

Confidence Intervals In Survival Analysis, Tan Shay Kee

Student Works (2010-2019)

In obtaining confidence interval for the survivor function using Greenwood’s formula and in performing log-rank test for comparing the survivor functions of two groups of individuals, only the information given by the first two moments of the relevant statistics are used. Presently we show that by incorporating the information given by the third and fourth moments of the statistics, the performance of the confidence interval and statistical test can be improved. When the survivor function can be described by the Weibull distribution, the knowledge regarding the survivor function can be obtained through the estimation of the Weibull scale and shape …

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A Markov Transition Model To Dementia With Death As A Competing Event, Liou Xu Jan 2010

A Markov Transition Model To Dementia With Death As A Competing Event, Liou Xu

University of Kentucky Doctoral Dissertations

The research on multi-state Markov transition model is motivated by the nature of the longitudinal data from the Nun Study (Snowdon, 1997), and similar information on the BRAiNS cohort (Salazar, 2004). Our goal is to develop a flexible methodology for handling the categorical longitudinal responses and competing risks time-to-event that characterizes the features of the data for research on dementia. To do so, we treat the survival from death as a continuous variable rather than defining death as a competing absorbing state to dementia. We assume that within each subject the survival component and the Markov process are linked by …

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Comparison Of Two Samples By A Nonparametric Likelihood-Ratio Test, William H. Barton Jan 2010

Comparison Of Two Samples By A Nonparametric Likelihood-Ratio Test, William H. Barton

University of Kentucky Doctoral Dissertations

In this dissertation we present a novel computational method, as well as its software implementation, to compare two samples by a nonparametric likelihood-ratio test. The basis of the comparison is a mean-type hypothesis. The software is written in the R-language [4]. The two samples are assumed to be independent. Their distributions, which are assumed to be unknown, may be discrete or continuous. The samples may be uncensored, right-censored, left-censored, or doubly-censored. Two software programs are offered. The first program covers the case of a single mean-type hypothesis. The second program covers the case of multiple mean-type hypotheses. For the first …

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Nonparametric Estimation Of Derivatives With Applications, Benjamin Hall Jan 2010

Nonparametric Estimation Of Derivatives With Applications, Benjamin Hall

University of Kentucky Doctoral Dissertations

We review several nonparametric regression techniques and discuss their various strengths and weaknesses with an emphasis on derivative estimation and confidence band creation. We develop a generalized C(p) criterion for tuning parameter selection when interest lies in estimating one or more derivatives and the estimator is both linear in the observed responses and self-consistent. We propose a method for constructing simultaneous confidence bands for the mean response and one or more derivatives, where simultaneous now refers both to values of the covariate and to all derivatives under consideration. In addition we generalize the simultaneous confidence bands to account for heteroscedastic …

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