Statistics and Probability Commons^™

Varieties Of P-Restriction Semigroups (2014), Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The restriction semigroups, in both their one-sided and two-sided versions, have arisen in various fashions, meriting study for their own sake. From one historical perspective, as “weakly E-ample” semigroups, the definition revolves around a “designated set” of commuting idempotents, better thought of as projections. This class includes the inverse semigroups in a natural fashion. In a recent paper, the author introduced P-restriction semigroups in order to broaden the notion of “projection” (thereby encompassing the regular *-semigroups). That study is continued here from the varietal perspective introduced for restriction semigroups by V. Gould. The relationship between varieties of regular …

Evaluating The Impact Of Genotype Errors On Rare Variant Tests Of Association, Kaitlyn Cook, Alejandra Benitez, Casey Fu, Nathan Tintle

Statistical and Data Sciences: Faculty Publications

The new class of rare variant tests has usually been evaluated assuming perfect genotype information. In reality, rare variant genotypes may be incorrect, and so rare variant tests should be robust to imperfect data. Errors and uncertainty in SNP genotyping are already known to dramatically impact statistical power for single marker tests on common variants and, in some cases, inflate the type I error rate. Recent results show that uncertainty in genotype calls derived from sequencing reads are dependent on several factors, including read depth, calling algorithm, number of alleles present in the sample, and the frequency at which an …

Statistical Analysis Of Depression And Social Support Change In Arab Immigrant Women In Usa, Hazhar Blbas

Electronic Theses and Dissertations

Arab Muslim immigrant women encounter many stressors and are at risk for depression. Social supports from husbands, family and friends are generally considered mitigating resources for depression. However, changes in social support over time and the effects of such supports on depression at a future time period have not been fully addressed in the literature This thesis investigated the relationship between demographic characteristics, changes in social support, and depression in Arab Muslim immigrant women to the USA. A sample of 454 married Arab Muslim immigrant women provided demographic data, scores on social support variables and depression at three time periods …

Markov Chain Theory With Applications To Baseball, Cal D. Thomay

Senior Independent Study Theses

The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing …

Introduction To Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate.

In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of …

The Efficient Use Of Supplementary Information In Finite Population Sampling, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are …

Fusion Of Masses Defined On Infinite Countable Frames Of Discernment, Florentin Smarandache, Arnaud Martin

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the fusion of information on infinite discrete frames of discernment and we give general results of the fusion of two such masses using the Dempster’s rule and the PCR5 rule for Bayesian and non-Bayesian cases.

A General Procedure Of Estimating Population Mean Using Information On Auxiliary Attribute, Sachin Malik, Rajesh Singh, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper deals with the problem of estimating the finite population mean when some information on auxiliary attribute is available. It is shown that the proposed estimator is more efficient than the usual mean estimator and other existing estimators. The results have been illustrated numerically by taking empirical population considered in the literature.

A Generalized Family Of Estimators For Estimating Population Mean Using Two Auxiliary Attributes, Sachin Malik, Rajesh Singh, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper deals with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. A class of estimators is defined which includes the estimators recently proposed by Malik and Singh (2012), Naik and Gupta (1996) and Singh et al. (2007) as particular cases. It is shown that the proposed estimator is more efficient than the usual mean estimator and other existing estimators. The study is also extended to two-phase sampling. The results have been illustrated numerically by taking empirical population considered in the literature.

Testing Longitudinal Data By Logarithmic Quantiles, Manfred Denker, Lucia Tabacu

Mathematics & Statistics Faculty Publications

The shoulder tip pain study of Lumley [13] is re-investigated. It is shown that the new logarithmic quantile estimation (LQE) technique in [9] applies and behaves well under singular covariance structure and small sample sizes as in the shoulder tip pain study. The findings in [6] can be assured under weaker assumptions using a combination of LQE and an ANOVA type statistic. © 2014, Institute of Mathematical Statistics.

Calculating P-Values, Isela Guerra

A with Honors Projects

For a Parkland College A with Honors project, the student tests a variety of methods to determine p-values.

Contaminated Chi-Square Modeling And Its Application In Microarray Data Analysis, Feng Zhou

Theses and Dissertations--Statistics

Mixture modeling has numerous applications. One particular interest is microarray data analysis. My dissertation research is focused on the Contaminated Chi-Square (CCS) Modeling and its application in microarray. A moment-based method and two likelihood-based methods including Modified Likelihood Ratio Test (MLRT) and Expectation-Maximization (EM) Test are developed for testing the omnibus null hypothesis of no contamination of a central chi-square distribution by a non-central Chi-Square distribution. When the omnibus null hypothesis is rejected, we further developed the moment-based test and the EM test for testing an extra component to the Contaminated Chi-Square (CCS+EC) Model. The moment-based approach is easy and …

Genetic Association Testing Of Copy Number Variation, Yinglei Li

Theses and Dissertations--Statistics

Copy-number variation (CNV) has been implicated in many complex diseases. It is of great interest to detect and locate such regions through genetic association testings. However, the association testings are complicated by the fact that CNVs usually span multiple markers and thus such markers are correlated to each other. To overcome the difficulty, it is desirable to pool information across the markers. In this thesis, we propose a kernel-based method for aggregation of marker-level tests, in which first we obtain a bunch of p-values through association tests for every marker and then the association test involving CNV is based on …

Natural Phenomena As Potential Influence On Social And Political Behavior: The Earth’S Magnetic Field, Jackie R. East

Theses and Dissertations--Political Science

Researchers use natural phenomena in a number of disciplines to help explain human behavioral outcomes. Research regarding the potential effects of magnetic fields on animal and human behavior indicates that fields could influence outcomes of interest to social scientists. Tests so far have been limited in scope. This work is a preliminary evaluation of whether the earth’s magnetic field influences human behavior it examines the baseline relationship exhibited between geomagnetic readings and a host of social and political outcomes. The emphasis on breadth of topical coverage in these statistical trials, rather than on depth of development for any one model, …

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Mathematics Faculty Publications

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Mathematics Faculty Publications

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation.

Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

Measuring Security: A Challenge For The Generation, Janusz Zalewski, Steven Drager, William Mckeever, Andrew J. Kornecki

Department of Electrical Engineering and Computer Science - Daytona Beach

This paper presents an approach to measuring computer security understood as a system property, in the category of similar properties, such as safety, reliability, dependability, resilience, etc. First, a historical discussion of measurements is presented, beginning with views of Hermann von Helmholtz in his 19th century work “Zählen und Messen”. Then, contemporary approaches related to the principles of measuring software properties are discussed, with emphasis on statistical, physical and software models. A distinction between metrics and measures is made to clarify the concepts. A brief overview of inadequacies of methods and techniques to evaluate computer security is presented, followed by …

A Fault-Based Model Of Fault Localization Techniques, Mark A. Hays

Theses and Dissertations--Computer Science

Every day, ordinary people depend on software working properly. We take it for granted; from banking software, to railroad switching software, to flight control software, to software that controls medical devices such as pacemakers or even gas pumps, our lives are touched by software that we expect to work. It is well known that the main technique/activity used to ensure the quality of software is testing. Often it is the only quality assurance activity undertaken, making it that much more important.

In a typical experiment studying these techniques, a researcher will intentionally seed a fault (intentionally breaking the functionality of …

Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng

Mathematics and Statistics Faculty Publications

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the “core” of the solution has multiple connected components, whose boundary called free boundary of the problems consists approximately of spheres which shrink to distinct single points as the parameter tends to zero.

Oldtimers & Newcomers In Collective Action, Stefanie R. Chamberlain

Theses and Dissertations

Most work on groups facing collective action assumes that group membership is static, or fixed. Yet static membership is rare, with members joining and leaving groups. In this thesis, I propose to explore how the presence of newcomers to groups affects group coordination. Past research has shown an overall negative effect of newcomers on group contributions. The proposed thesis attempts to further establish the effect by determining whether newcomers, oldtimers, or both are responsible for the declining cooperation in groups. While the empirical component is focused solely on establishing who is responsible for driving down cooperation rates in dynamic groups, …

Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang

College of Graduate Studies: Theses & Dissertations

Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, …

Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina

College of Graduate Studies: Theses & Dissertations

In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included …

An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun

College of Graduate Studies: Theses & Dissertations

Change point is a statistic phenomenon, which has many direct applications in climatology, bioinformatics, finance, oceanography and medical imaging. In this thesis, we investigate the sensitivity of the F-test for detecting change points in linear regression, using a two-phase linear regression model. it offers an effective method to detect "undocumented" change points using a form of an F-test. Using simulated data, we explore its sensitivity and accuracy with respect t different parameters in the model.

Normal Mixture And Contaminated Model With Nuisance Parameter And Applications, Qian Fan

Theses and Dissertations--Statistics

This paper intend to find the proper hypothesis and test statistic for testing existence of bilaterally contamination when there exists nuisance parameter. The test statistic is based on method of moments estimators. Union-Intersection test is used for testing if the distribution of population can be implemented by a bilaterally contaminated normal model with unknown variance. This paper also developed a hierarchical normal mixture model (HNM) and applied it to birth weight data. EM algorithm is employed for parameter estimation and a singular Bayesian information criterion (sBIC) is applied to choose the number components. We also proposed a singular flexible information …

Value Of Mendelian Laws Of Segregation In Families: Data Quality Control, Imputation, And Beyond, Elizabeth M. Blue, Lei Sun, Nathan L. Tintle, Ellen M. Wijsman

Faculty Work Comprehensive List

When analyzing family data, we dream of perfectly informative data, even whole-genome sequences (WGSs) for all family members. Reality intervenes, and we find that next-generation sequencing (NGS) data have errors and are often too expensive or impossible to collect on everyone. The Genetic Analysis Workshop 18 working groups on quality control and dropping WGSs through families using a genome-wide association framework focused on finding, correcting, and using errors within the available sequence and family data, developing methods to infer and analyze missing sequence data among relatives, and testing for linkage and association with simulated blood pressure. We found that single-nucleotide …

Pathway Analysis Approaches For Rare And Common Variants: Insights From Genetic Analysis Workshop 18, Stella Aslibekyan, Marcio Almeida, Nathan L. Tintle

Faculty Work Comprehensive List

Pathway analysis, broadly defined as a group of methods incorporating a priori biological information from public databases, has emerged as a promising approach for analyzing high-dimensional genomic data. As part of Genetic Analysis Workshop 18, seven research groups applied pathway analysis techniques to whole-genome sequence data from the San Antonio Family Study. Overall, the groups found that the potential of pathway analysis to improve detection of causal variants by lowering the multiple-testing burden and incorporating biologic insight remains largely unrealized. Specifically, there is a lack of best practices at each stage of the pathway approach: annotation, analysis, interpretation, and follow-up. …

Statistical Analysis Of Sleep Patterns In Drosophila Melanogaster, Luyang Wang

Masters Theses

“Sleep is one of the most preserved and restorative behaviors of animals and is important in human health. Lack of sleep may cause numerous diseases. So the study of sleep rhythms is very essential and complicated. In order to simplify the process of studying sleep, the fruit fly Drosophila melanogaster, is utilized as a model organism for several reasons. Some of the molecular mechanisms that contribute to the circadian clock in the fruit fly were also found to generate similar cycles in mammals. In order to study sleep patterns in the fruit fly, experiments were designed and performed to …

Building A Predictive Model For Baseball Games, Jordan Robertson Tait

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …

Indemics: An Interactive High-Performance Computing Framework For Data Intensive Epidemic Modeling, Keith R. Bisset, Jiangzhuo Chen, Suruchi Deodhar, Xizhou Feng, Yifei Ma, Madhav V. Marathe

Mathematics, Statistics and Computer Science Faculty Research and Publications

We describe the design and prototype implementation of Indemics (_Interactive; Epi_demic; _Simulation;)—a modeling environment utilizing high-performance computing technologies for supporting complex epidemic simulations. Indemics can support policy analysts and epidemiologists interested in planning and control of pandemics. Indemics goes beyond traditional epidemic simulations by providing a simple and powerful way to represent and analyze policy-based as well as individual-based adaptive interventions. Users can also stop the simulation at any point, assess the state of the simulated system, and add additional interventions. Indemics is available to end-users via a web-based interface.

Detailed performance analysis shows that Indemics greatly enhances the …

The Impact Of Nested Testing On Experiment-Wise Type I Error Rate, Jack Sawilowsky

Wayne State University Dissertations

When conducting a statistical test the initial risk that must be considered is a Type I error, also known as a false positive. The Type I error rate is set by nominal alpha, assuming all underlying conditions of the statistic are met. Experiment-wise Type I error inflation occurs when multiple tests are conducted overall for a single experiment. There is a growing trend in the social and behavioral sciences utilizing nested designs. A Monte Carlo study was conducted using a two layer design. Five theoretical distributions and four real datasets taken from Micceri (1989) were used, each with five different …