Statistics and Probability Commons^™

The Transmuted Weibull-Pareto Distribution, Ahmed Z. Afify, Haitham M. Yousof, Nadeem Shafique Butt, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set.

Diversification And Market Neutral Portfolios In S&P500, Alan S. Agnew

Williams Honors College, Honors Research Projects

Our goal is to investigate strategies to deal with the risks associated with holding asset in the stock market. We first deal with risk of holding a specific stock, by the use of diversification. Later, we’ll attempt to deal with the market risk, which is the risk of entire market going up and down. Data used in this project comes from daily adjusted closing price of stocks listed in the S&P500 index ranging from January 3^rd, 2000 to December 31^st, 2015 and the data is processed using statistical software R.

Sections 2 through 4 of this …

Development Of Efficient Simultaneous Confidence Bounds For Linear Mixed Models With Applications In Alcohol Research, Emmanuel Joseph Sequeira

Open Access Theses & Dissertations

Multiplicity corrections are necessary to ensure the accuracy of conclusions made in studies that carry out multiple inferences simultaneously. This Thesis uses the methodology derived by Hunter and Worsley to obtain improved simultaneous confidence bounds (SCBs) that are less conservative than the highly used Bonferroni SCBs, for studies using linear mixed modeling. Empirical coverage rates were obtained for data that was generated using simulations, to compare the accuracy of the Hunter-Worsley SCBs with that of the Bonferroni SCBs. The bounds were also applied to data in the field of alcohol research, where comparisons were made to determine the moderating effect …

Pre-Tuned Principal Component Regression And Several Variants, Pei Wang

Open Access Theses & Dissertations

The regression coecient estimates from ordinary least squares (OLS) have a low probability of being close to the real value when there is a multicollinearity problem in the design matrix. In order to combat this problem, many regularized methods have been introduced. Principal components regression (PCR) is an important analysis tool for dealing with multicollinearity and high-dimensionality. In conventional PCR, the rst step is to change the original predictors to orthogonal principal components (PC's) by a linear transformation. These PC's correspond to the eigenvalues which are sorted in a decreasing order. The next step is to regress the response on …

Black Cloud Randomization Test, Nicholas S. Vanni

Williams Honors College, Honors Research Projects

The Black Cloud Randomization Test looks at a nontraditional question and attempts to answer the question using unique statistics. The purpose of this paper is to apply what has been learned throughout the years and apply this knowledge to a final project. Data for this project follows an emergency room’s on call schedule, as well as the number of traumas that came in during each day shift. The project builds on what has been already learned and helps to open a different way of working with statistics. The project was coded in the R software. With different restrictions, there are …

Distribution-Free Trends Test To Determine The Construct Validity Of An Anti-Social Criminal Attitudes Scale, Holly Ann Child

Wayne State University Dissertations

The Sawilosky's I-Test was developed to as an alternative method to evaluate construct validity, more specifically, in regards to the Multitrait-Multimethod Matrix designed by Campbell and Fiske (1959). Typically, researchers use a method by Campbell and Fiske that involves a subjective “physical” look at the matrix to determine validity. Sawilowsky’s I-Test offers a statistical approach that incorporates the current practice but removes the subjectivity involved in this process.

There are only two existing studies that look at the I-Test, Sawilowsky in 2002 and Cuzzocrea in 2007. Both studies found that although the I-Test is not a perfect statistic, it provides …

The Impact Of Multiple Imputation On The Type Ii Error Rate Of The T Test, Tammy A. Grace

Wayne State University Dissertations

ABSTRACT

THE IMPACT OF MULTIPLE IMPUTATION ON THE TYPE II ERROR RATE OF

THE T TEST

by

TAMMY A. GRACE

August 2016

Advisor: Shlomo Sawilowsky, PhD

Major: Evaluation and Research

Degree: Doctor of Philosophy

The National Academy of Science identified numerous high priority areas for missing data research. This study addresses several of those areas by systematically investigating the impact of multiple imputation on the rejection rate of the independent samples t test under varying conditions of sample size, effect size, fraction of missing data, distribution shape, and alpha. In addition to addressing gaps in the missing data literature, this …

Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd

College of Graduate Studies: Theses & Dissertations

Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.

Consistency Of Cheeger And Ratio Graph Cuts, Nicolas Garcia Trillos, Dejan Slepcev, James Von Brecht, Thomas Laurent, Xavier Bresson

Mathematics, Statistics and Data Science Faculty Works

This paper establishes the consistency of a family of graph-cut- based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be …

Non-Conventional Approaches To Syntheses Of Ferromagnetic Nanomaterials, Dustin M. Clifford

Theses and Dissertations

The work of this dissertation is centered on two non-conventional synthetic approaches to ferromagnetic nanomaterials: high-throughput experimentation (HTE) (polyol process) and continuous flow (CF) synthesis (aqueous reduction and the polyol process). HTE was performed to investigate phase control between Fe_xCo_1-x and Co_3-xFe_xO_y. Exploration of synthesis limitations based on magnetic properties was achieved by reproducing M_s=210 emu/g. Morphological control of Fe_xCo_1-x alloy was achieved by formation of linear chains using an H_ext. The final study of the Fe_xCo_1-x chains used DoE to …

An Online Statistics Course From Faculty And Students' Perspectives: A Case Study, Ruth Best

Walden Dissertations and Doctoral Studies

Faculty at a private college in the northeastern United States found students lacked prerequisite mathematical skills and were unable to transfer quantitative reasoning skills to upper level business courses. Guided by Mezirow's transformative learning theory and Knowles' approach to self-directed learning, this study examined how undergraduate students learn statistics online. The purpose of this qualitative embedded case study was to examine faculty and students' perspectives about the online statistics course design and delivery while exploring possible barriers to students' learning. Data collection occurred by review of course documents and the learning management system. Archival data generated questions for semistructured interviews …

Finding The Cutpoint Of A Continuous Covariate In A Parametric Survival Analysis Model, Kabita Joshi

Theses and Dissertations

In many clinical studies, continuous variables such as age, blood pressure and cholesterol are measured and analyzed. Often clinicians prefer to categorize these continuous variables into different groups, such as low and high risk groups. The goal of this work is to find the cutpoint of a continuous variable where the transition occurs from low to high risk group. Different methods have been published in literature to find such a cutpoint. We extended the methods of Contal and O’Quigley (1999) which was based on the log-rank test and the methods of Klein and Wu (2004) which was based on the …

Powerful Association Test Combining Rare Variant And Gene Expression Using Family Data From Genetic Analysis Workshop 19, Yen Yi Ho, Weihua Guan, Michael O'Connell, Saonli Basu

Faculty Publications

Background: Genetic association studies aim to test for disease or trait association with genetic variants, either throughout the human genome or in regions of interest. However, for most diseases and traits, the combined effects of associated genetic variants explain only a small proportion of the genetic variation. This "missing heritability" may be a result of the small effects of common variants considered in the genetic association studies. Rare variants may also play an important role in understanding the missing heritability of complex traits. Method: We propose a novel weight-adjustment approach to combine gene expression into rare variant analysis. Results from …

Sample Size Calculation For Ph Mixture Cure Model, Yihong Zhan

Theses and Dissertations

With the development of advanced medical technology, a significant proportion of patients can be cured of many chronic diseases. Because a substantial fraction of patients have censored information, the standard survival model, such as the proportional hazards (PH) model cannot capture the cured information of patients. Thus PH mixture cure model is developed to handle the survival data with potential cured information. A corresponding sample size formula based on log rank test has been proposed by Wang et al. (2012) and the probability of death in their formula is only contributed by the control arm. However, to calculate the sample …

Parametric Reversed Hazards Model For Left Censored Data With Application To Hiv, Farahnaz Islam

Theses and Dissertations

Left censoring is generally a rare type of censoring in time-to-event data, however there are some fields such as HIV related studies where it commonly occurs. Currently, there is no clear recommendation in the literature on the optimal model and distribution to analyze left-censored data. Recommendations can help researchers apply more accurate models for this type of censoring. This study derives the Parametric Reversed Hazards (PRH) Model for a variety of distributions which may be appropriate for left censored data. The performance of these derived PRH models to analyze HIV viral load data are compared using extensive simulations and a …

Doing Qualitative Research Online Book Review, Donna M. Busarow

Journal of Social, Behavioral, and Health Sciences

A recent addition to qualitative instruction is Salmon's (2016) book, Doing Qualitative Research Online. This book review examines the book as an educational tool for student researchers.

Resolving Gnetum Evolutionary History, Angela Mcfadden

All Master's Theses

Gnetum are non-flowering seed plants of the tropics, indigenous to South America, Africa, and Asia. This group of about 40 species is fascinating to botanists because it shares distinctive morphological characteristics with flowering plants, such as broad leaves, woody stems, and flower-like strobili. There are still questions surrounding the relationships within the genus of Gnetum. With that in mind, I focused my work on generating phylogenetic hypotheses, using two molecular data sets: a concatenation of over 60 different chloroplast genes (66,815 base pairs), and the whole chloroplast genome (128,772 base pairs). This allowed me to compare the two phylogenies …

Anatomy, Implant Selection And Placement Influence Spine Mechanics Associated With Total Disc Replacement, Justin F.M. Hollenbeck

Electronic Theses and Dissertations

Through aging and injury, the intervertebral disc of the lumbar spine can undergo degeneration, leading to collapse of the vertebrae and low back pain, a symptom that affects half the adult population in any given year. In an effort to reduce low back pain, total disc replacement treatment removes the degenerated disc, restores natural height and lordosis of the segment, and preserves motion at the joint. Patient anatomy, implant selection, and implant placement play significant roles in a patient's outcomes after total disc replacement surgery. Thus, the objective of the work presented in this thesis was to develop a suite …

Missing Data In Clinical Trial: A Critical Look At The Proportionality Of Mnar And Mar Assumptions For Multiple Imputation, Theophile B. Dipita

College of Graduate Studies: Theses & Dissertations

Randomized control trial is a gold standard of research studies. Randomization helps reduce bias and infer causality. One constraint of these studies is that it depends on participants to obtain the desired data. Whatever the researcher can do, there is a possibility to end up with incomplete data. The problem is more relevant in clinical trials when missing data can be related to the condition under study. The benefits of randomization is compromised by missing data. Multiple imputation is a valid method of treating missing data under the assumption of MAR. Unfortunately this is an unverified assumptions. Current practice advise …

Impairment Of Continuous Insulin Delivery Therapy And Analysis From Graeco-Latin Square Design Model, Norou Diawara, Ayodeji Demuren, Eric Gyuricsko

Mathematics & Statistics Faculty Publications

The desire to deliver measured amount of insulin continuously to patients with type I diabetes, for glycemic control, has attracted a lot of attention. Continuous subcutaneous insulin infusion has seen some success in recent years. However, occlusion of insulin delivery may prevent the patient from receiving the prescribed dosage, with adverse consequence. An in vitro study of insulin delivery is performed, using different insulin pumps, insulin analogs and operating conditions. The aim is to identify incidences of occlusion due to bubble formation in the infusion line. A detailed statistical analysis was performed on the data collected to determine any significant …

Modeling Spatially Varying Effects Of Chemical Mixtures, Jenna Czarnota

Theses and Dissertations

Cancer incidence is associated with exposures to multiple environmental chemicals, and geographic variation in cancer rates suggests the importance of accommodating spatially varying effects in the analysis of environmental chemical mixtures and disease risk. Traditional regression methods are challenged by the complex correlation patterns inherent among co-occurring chemicals, and the applicability of geographically weighted regression models is limited in the setting of environmental chemical risk analysis. In comparison to traditional methods, weighted quantile sum (WQS) regression performs well in the identification of important environmental exposures, but is limited by the assumption that effects are fixed over space. We present an …

Data Analytics On Consumer Behavior In Omni-Channel Retail Banking, Card And Payment Services, Geng Dan

Research Collection School Of Computing and Information Systems

Innovations in financial services have created challenges for banks that Information Systems (IS) research can address. My interests involve transaction cost theory, substitution and complementarity theory, and consumer informedness theory to understand consumer behavior and firm performance in the omni-channel world of digital banking. At a high level, my research inquiry asks: How can financial institutions take advantage of the deep insights that data analytics and management science modeling create on consumer behavior and channel management decision-making? And how can changes in payments and services in retail banking be understood in spatial and temporal terms? I am working on three …

Effect Of An Interactive Component On Students' Conceptual Understanding Of Hypothesis Testing, Sarah Anne Inkpen

Walden Dissertations and Doctoral Studies

The Premier Technical College of Qatar (PTC-Q) has seen high failure rates among students taking a college statistics course. The students are English as a foreign language (EFL) learners in business studies and health sciences. Course delivery has involved conventional content/curriculum-centered instruction with minimal to no interactive components. The purpose of this quasi-experimental study was to assess the effectiveness of an interactive approach to teaching and learning statistics used in North America and the United Kingdom when used with EFL students in the Middle East. Guided by von Glasersfeld's constructivist framework, this study compared conceptual understanding between a convenience sample …

The Association Between Osteoporosis And Early Menopause Following Hysterectomy, Mia Meeyaong-Won Botkin

Walden Dissertations and Doctoral Studies

Osteoporosis is considered to be the most adverse public health disease associated with substantial mortality among postmenopausal women. Hysterectomy, surgically induced menopause, contributes to the early onset of menopause. However, there was no evidence of an association between early menopause following hysterectomy and osteoporosis among postmenopausal women. The purpose of this quantitative study was to examine the association between demographic and behavioral factors and the prevalence of osteoporosis among hysterectomized postmenopausal women. The integrated theory of health behavior change theoretical framework guided study. Cross-sectional secondary data from the 2009-2010 National Health and Nutrition Examination Survey were used. Multiple logistic regression …

Early Sex Work Initiation And Condom Use Among Alcohol-Using Female Sex Workers In Mombasa, Kenya: A Cross-Sectional Analysis, A. M. Parcesepe, Kelly L'Engle, S. L. Martin, S. Green, C. Suchindran, P. Mwarogo

Nursing and Health Professions Faculty Research and Publications

Objectives Early initiation of sex work is prevalent among female sex workers (FSWs) worldwide. The objectives of this study were to investigate if early initiation of sex work was associated with: (1) consistent condom use, (2) condom negotiation self-efficacy or (3) condom use norms among alcohol-using FSWs in Mombasa, Kenya.

Methods In-person interviews were conducted with 816 FSWs in Mombasa, Kenya. Sample participants were: recruited from HIV prevention drop-in centres, 18 years or older and moderate risk drinkers. Early initiation was defined as first engaging in sex work at 17 years or younger. Logistic regression modelled outcomes as a function …

Registration And Clustering Of Functional Observations, Zizhen Wu

Theses and Dissertations

As an important exploratory analysis, curves of similar shape are often classified into groups, which we call clustering of functional data. Phase variations or time distortions are often encountered in the biological processes, such as growth patterns or gene profiles. As a result of time distortion, curves of similar shape may not be aligned. Regular clustering methods for functional data usually ignore the presence of phase variations, which may result in low clustering accuracy. However, it is difficult to account for phase variation without knowing the cluster structure.

In this dissertation, we first propose a Bayesian method that simultaneously clusters …

Modern Estimation Problems In Group Testing, Md Shamim Sarker

Theses and Dissertations

In the simplest form of group testing, pools are formed by compositing a fixed number of individual specimens (e.g., blood, urine, swab, etc.) and then the pools are tested for a binary characteristic, such as presence or absence of a disease. Group testing is commonly used to screen for a variety of sexually transmitted diseases in epidemiological applications where the main goal is to increase testing efficiency. In this dissertation, we study three estimation problems that are motivated by real-life applications. We propose new methods to model group testing data for both single and multiple infections. In the first problem, …

Semiparametric Joint Dynamic Modeling Of A Longitudinal Marker, Recurrent Competing Risks, And A Terminal Event, Piaomu Liu

Theses and Dissertations

The joint modeling framework has found extensive applications in cancer and other biomedical research. For example, recent initiatives and developments in precision medicine call for appropriate prognostic tools to assist individualized or personalized approaches in cancer diagnosis and treatment. Data generated by clinical trials and medical research often include correlated longitudinal marker measurements and time- to-event information, which are possibly a recurrent event, competing risks, and a survival outcome. Primary interests of joint modeling include the association between the longitudinal marker measurements and time-to-event data, as well as predictions of survival probabilities of new observational units from the same population. …

Spatio-Temporal Analysis Of The Occupational Fatal Victimization Of Law Enforcement Officers In The Us, Xueyi Xing

Theses and Dissertations

The models with constant coefficients of the covariates across space and time are commonly used in spatio-temporal analyses. However, the associations between risk factors and the outcome could have locally differential temporal trends in many cases. In this study, a Bayesian latent cluster modeling strategy is employed to identify potential spatial clusters in which locally specific sets of temporally varying coefficients of covariates are allowed. A state-level panel data of police officers occupational fatal victimization for the years 1979-2010 is used. To accommodate overdisperson and excess zeros, a negative binomial model and zero-inflated Poisson/negative binomial models are also utilized. A …

Regression Models For Count Data Based On The Double Poisson Distribution, Rebecca Wardrop

Theses and Dissertations

This paper explores the double Poisson distribution. The probability mass function and the difficulties associated with derivative-based optimization for this distribution are discussed. Stata software developed for estimation of double Poisson regression is detailed. Simulations are used to test the software. Data which are over-, under-, and equidispersed relative to the Poisson are generated and the software is utilized to estimate a regression model, a zero-inflated model, and a marginalized zero-inflated model all based on the double Poisson distribution. The estimated power of the test for φ = 1 for the double Poisson models are compared to the power of …