Statistics and Probability Commons^™

On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The sum of independent, but not necessary identically distributed, exponential random variables follows a hypoexponential distribution. We focus on a particular case when all but one rate parameters of the exponential variables are identical. This is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.

Controlled Branching Processes With Continuous Time, Miguel Gonzalez, Manuel Molina, Ines Del Puerto, Nikolay Yanev, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

Continuous-Time Controlled Branching Processes, Ines Garcia, George Yanev, Manuel Molina, Nikolay Yanev, Miguel Velasco

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Controlled branching processes with continuous time are introduced and limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n ≥ 2, X1, X2, . . . , Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj ’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently …

Extreme Events And Emergency Scales, Veniamin Smirnov, Zhuanzhuan Ma, Dimitri Volchenkov

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

An event is extreme if its magnitude exceeds the threshold. A choice of a threshold is subject to uncertainty caused by a method, the size of available data, a hypothesis on statistics, etc. We assess the degree of uncertainty by the Shannon's entropy calculated on the probability that the threshold changes at any given time. If the amount of data is not sufficient, an observer is in the state of Lewis Carroll's Red Queen who said "When you say hill, I could show you hills, in comparison with which you'd call that a valley". If we have enough data, the …

On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Arnold and Villasenor [4] obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from [4], we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.

Sex And Age Differences In Prevalence And Risk Factors For Prediabetes In Mexican-Americans, Kristina Vatcheva, Belinda M. Reininger, Susan P. Fisher-Hoch, Joseph B. Mccormick

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

AIMS:

Over 1/3 of Americans have prediabetes, while 9.4% have type 2 diabetes. The aim of our study was to estimate the prevalence of prediabetes in Mexican Americans, with known 28.2% prevalence of type 2 diabetes, by age and sex and to identify critical socio-demographic and clinical factors associated with prediabetes.

METHODS:

Data were collected between 2004 and 2017 from the Cameron County Hispanic Cohort in Texas. Weighted crude and sex- and age- stratified prevalences were calculated. Survey weighted logistic regression analyses were conducted to identify risk factors for prediabetes.

RESULTS:

The prevalence of prediabetes (32%) was slightly higher than …

Examining The Prevalence Rates Of Preexisting Maternal Medical Conditions And Pregnancy Complications By Source: Evidence To Inform Maternal And Child Research, Candace A. Robledo, Edwina H. Yeung, Pauline Mendola, Rajeshwari Sundaram, Nansi S. Boghossian, Erin M. Bell, Charlotte Druschel

School of Medicine Publications and Presentations

Objectives—We sought to examine whether there are systematic differences in ascertainment of preexisting maternal medical conditions and pregnancy complications from three common data sources used in epidemiologic research

Methods—Diabetes mellitus, chronic hypertension, gestational diabetes mellitus (GDM), gestational hypertensive disorders (GHD), placental abruption and premature rupture of membranes (PROM) among 4821 pregnancies were identified via birth certificates, maternal self-report at approximately 4 months postpartum and by discharge codes from the Statewide Planning and Research Cooperative System (SPARCS), a mandatory New York State hospital reporting system. The kappa statistic (k) was estimated to ascertain beyond chance agreement of outcomes between birth certificates …

Statistical Modeling Of Microrna Expression With Human Cancers, Ke-Sheng Wang, Yue Pan, Chun Xu

Health & Biomedical Sciences Faculty Publications and Presentations

MicroRNAs (miRNAs) are small non-coding RNAs (containing about 22 nucleotides) that regulate gene expression. MiRNAs are involved in many different biological processes such as cell proliferation, differentiation, apoptosis, fat metabolism, and human cancer genes; while miRNAs may function as candidates for diagnostic and prognostic biomarkers and predictors of drug response. This paper emphasizes the statistical methods in the analysis of the associations of miRNA gene expression with human cancers and related clinical phenotypes: 1) simple statistical methods include chi-square test, correlation analysis, t-test and one-way ANOVA; 2) regression models include linear and logistic regression; 3) survival analysis approaches such as …