Statistics and Probability Commons^™

A Monte Carlo Study Of The Effects Of Variability And Outliers On The Linear Correlation Coefficient, Hussein Yousif Eledum

Journal of Modern Applied Statistical Methods

Monte Carlo simulations are used to investigate the effect of two factors, the amount of variability and an outlier, on the size of the Pearson correlation coefficient. Some simulation algorithms are developed, and two theorems for increasing or decreasing the amount of variability are suggested.

Parameter Estimation In Weighted Rayleigh Distribution, M. Ajami, S. M. A. Jahanshahi

Journal of Modern Applied Statistical Methods

A weighted model based on the Rayleigh distribution is proposed and the statistical and reliability properties of this model are presented. Some non-Bayesian and Bayesian methods are used to estimate the β parameter of proposed model. The Bayes estimators are obtained under the symmetric (squared error) and the asymmetric (linear exponential) loss functions using non-informative and reciprocal gamma priors. The performance of the estimators is assessed on the basis of their biases and relative risks under the two above-mentioned loss functions. A simulation study is constructed to evaluate the ability of considered estimation methods. The suitability of the proposed model …

Jmasm 46: Algorithm For Comparison Of Robust Regression Methods In Multiple Linear Regression By Weighting Least Square Regression (Sas), Mohamad Shafiq, Wan Muhamad Amir, Nur Syabiha Zafakali

Journal of Modern Applied Statistical Methods

The aim of this study is to compare different robust regression methods in three main models of multiple linear regression and weighting multiple linear regression. An algorithm for weighting multiple linear regression by standard deviation and variance for combining different robust method is given in SAS along with an application.

Bayesian Hypothesis Testing Of Two Normal Samples Using Bootstrap Prior Technique, Oyebayo Ridwan Olaniran, Waheed Babatunde Yahya

Journal of Modern Applied Statistical Methods

The most important ingredient in Bayesian analysis is prior or prior distribution. A new prior determination method was developed under the framework of parametric empirical Bayes using bootstrap technique. By way of example, Bayesian estimations of the parameters of a normal distribution with unknown mean and unknown variance conditions were considered, as well as its application in comparing the means of two independent normal samples with several scenarios. A Monte Carlo study was conducted to illustrate the proposed procedure in estimation and hypothesis testing. Results from Monte Carlo studies showed that the bootstrap prior proposed is more efficient than the …

Sample Size Calculations And Normalization Methods For Rna-Seq Data., Xiaohong Li

Electronic Theses and Dissertations

High-throughput RNA sequencing (RNA-seq) has become the preferred choice for transcriptomics and gene expression studies. With the rapid growth of RNA-seq applications, sample size calculation methods for RNA-seq experiment design and data normalization methods for DEG analysis are important issues to be explored and discussed. The underlying theme of this dissertation is to develop novel sample size calculation methods in RNA-seq experiment design using test statistics. I have also proposed two novel normalization methods for analysis of RNA-seq data. In chapter one, I present the test statistical methods including Wald’s test, log-transformed Wald’s test and likelihood ratio test statistics for …

Survival Analysis: A Modified Kaplan-Meir Estimator, Justin A. Bancroft

Graduate Theses/Dissertations

The popular Kaplan-Meir estimator has traditionally been used to great effect as a survival function estimator. However, the Kaplan-Meir estimator is dependent upon a maximum likelihood parameter estimator which may not be the best estimator in all cases. We modify the Kaplan-Meir estimator, based on a Bayes parameter estimation, in hopes of providing a more accurate survival estimator for small sample sizes. Core elements of survival analysis are presented, acting as a foundation from which to construct and compare our modified Kaplan-Meir estimator. It is hypothesized that our modified Kaplan-Meir estimator is generally more accurate than the standard Kaplan-Meir estimator …

Reliability Of An Observational Method Used To Assess Tennis Serve Mechanics In A Group Of Novice Raters, Natalie L. Myers, W. Ben Kibler, Gilson J. Capilouto, Philip M. Westgate, Tony English, Timothy L. Uhl

Physical Therapy Faculty Publications

Background: Previous research has developed an observational tennis serve analysis (OTSA) tool to assess serve mechanics. The OTSA has displayed substantial agreement between the two health care professionals that developed the tool; however, it is currently unknown if the OTSA is reliable when administered by novice users.

Purpose: The purpose of this investigation was to determine if reliability for the OTSA could be established in novice users via an interactive classroom training session.

Methods: Eight observers underwent a classroom instructional training protocol highlighting the OTSA. Following training, observers participated in two different rating sessions approximately a week apart. Each observer …

The Role Of Pre-Existing Type 2 Diabetes Mellitus In Colorectal Cancer Stage And Survival In Elderly Americans: A Seer-Medicare Population-Based Study 2002-~2011, Sanae El Ibrahimi

UNLV Theses, Dissertations, Professional Papers, and Capstones

Diabetes is a common comorbid condition among colorectal cancer (CRC) patients, yet its effects in CRC outcomes, particularly stage at diagnosis, risk of death and variations by diabetes severity (complications vs no complications) and Hispanic ethnicity have not been adequately studied. The purpose of this study was to investigate the association between pre-existing T2DM and advanced stage at diagnosis in elderly patients with CRC; to examine whether diabetes is an independent predictor of poor survival from all-cause and CRC-specific mortality; to assess whether variations exist by diabetes severity and to analyze the outcomes for the Hispanic group.

The Surveillance Epidemiology …

The Impact Of Economic Recession On The Health Of Adult Nevadans, Ariana Goertz

UNLV Theses, Dissertations, Professional Papers, and Capstones

Recessions are generally considered to cause negative consequences, but recent studies have provided evidence that some health outcomes improve as the economy deteriorates. The relationship between economic downfalls and health is not straightforward; it is important to look at how health has been impacted in one of the areas hit hardest by the recession. Las Vegas, Nevada was previously considered recession-proof, seemingly unaffected by previous economic downturns exhibited by the rest of the country. However, during the Great Recession of 2007-2009, Las Vegas led the country in highest rates of unemployment and foreclosures. This was quite a collapse for a …

A Customized Quantitative Pcr Microrna Panel Provides A Technically Robust Context For Studying Neurodegenerative Disease Biomarkers And Indicates A High Correlation Between Cerebrospinal Fluid And Choroid Plexus Microrna Expression, Wang-Xia Wang, David W. Fardo, Gregory A. Jicha, Peter T. Nelson

Sanders-Brown Center on Aging Faculty Publications

MicroRNA (miRNA) expression varies in association with different tissue types and in diseases. Having been found in body fluids including blood and cerebrospinal fluid (CSF), miRNAs constitute potential biomarkers. CSF miRNAs have been proposed as biomarkers for neurodegenerative diseases; however, there is a lack of consensus about the best candidate miRNA biomarkers and there has been variability in results from different research centers, perhaps due to technical factors. Here, we sought to optimize technical parameters for CSF miRNA studies. We examined different RNA isolation methods and performed miRNA expression profiling with TaqMan® miRNA Arrays. More specifically, we developed a customized …

Functional Data Analysis Methods For Predicting Disease Status., Sarah Kendrick

Electronic Theses and Dissertations

Introduction: Differential scanning calorimetry (DSC) is used to determine thermally-induced conformational changes of biomolecules within a blood plasma sample. Recent research has indicated that DSC curves (or thermograms) may have different characteristics based on disease status and, thus, may be useful as a monitoring and diagnostic tool for some diseases. Since thermograms are curves measured over a range of temperature values, they are often considered as functional data. In this dissertation we propose and apply functional data analysis (FDA) techniques to analyze DSC data from the Lupus Family Registry and Repository (LFRR). The aim is to develop FDA methods to …

Transient Solution Of M[X1],M[X2]/G1,G2/1 With Priority Services, Modified Bernoulli Vacation, Bernoulli Feedback, Breakdown, Delaying Repair And Reneging, G. Ayyappan, J. Udayageetha

Applications and Applied Mathematics: An International Journal (AAM)

This paper considers a queuing system which facilitates a single server that serves two classes of units: high priority and low priority units. These two classes of units arrive at the system in two independent compound Poisson processes. It aims to decipher average queue size and average waiting time of the units. Under the pre-emptive priority rule, the server provides a general service to these arriving units. It is further assumed the server may take a vacation after serving the last high priority unit present in the system or at the service completion of each low priority unit present in …

Stationary Analysis Of A Multiserver Queue With Multiple Working Vacation And Impatient Customers, P. Manoharan, Shakir Majid

Applications and Applied Mathematics: An International Journal (AAM)

We consider an M/M/c queue with multiple working vacation and impatient customers. The server serves the customers at a lower rate rather than completely halts the service during this working vacation period. The impatience of the customer’s arises when they arrive during the working vacation period, where the service rate of the customer’s is lower than the normal busy period. The queue is analyzed for multiple working vacation policies. The policy of a MWV demands the server to keep taking vacation until it finds at least a single customer waiting in the system at an instant vacation completion. On returning …

Exponentiated Weibull-Exponential Distribution With Applications, M. Elgarhy, M. Shakil, B. M. Golam Kibria

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a new four-parameter continuous model, called the exponentiated Weibull exponential distribution, is introduced based on exponentiated Weibull-G family (Hassan and Elgarhy, 2016). The new model contains some new distributions as well as some former distributions. Various mathematical properties of this distribution are studied. General explicit expressions for the quantile function, expansion of distribution and density functions, moments, generating function, Rényi and q – entropies, and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. The practical importance of the new distribution is demonstrated through real data set where we compare …

Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali

Applications and Applied Mathematics: An International Journal (AAM)

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence.

Analysis Of A M/M/C Queue With Single And Multiple Synchronous Working Vacations, Shakir Majid, P. Manoharan

Applications and Applied Mathematics: An International Journal (AAM)

We consider a M/M/c queuing system with synchronous working vacation and two different policies of working vacation i.e. a multiple working vacation policy and a single working policy. During a working vacation the server does not completely halts the service rather than it will render service at a lower rate. In synchronous vacation policy all the servers leave for a vacation simultaneously, when the server finds the system empty after finishing serving a customer. In multiple working vacation (MWV) policy the servers continue to take vacation till they find the system nonempty at a vacation completion instant. Single working vacation …

Proportional Reversed Hazard Rate Models With Exponential Baseline, G. Barmalzan, H. Saboori

Applications and Applied Mathematics: An International Journal (AAM)

The proportional hazard regression models have been used extensively in survival analysis to understand and exploit the relationship between survival time and covariates. For left censored survival times, reversed hazard rate functions are more appropriate. In this paper, we discuss a parametric proportional reversed hazard rates model using exponential baseline. The estimation for the parameters are discussed. We also assess the performance of the proposed procedure based on a large number of Monte Carlo simulations. Finally, we illustrate the proposed method using a real case example and then we show that it provides a good and better fit than the …

On Some Statistics For Testing The Skewness In A Population: An Empirical Study, Yawen Guo, B. M. Golam Kibria

Applications and Applied Mathematics: An International Journal (AAM)

The purpose of this paper is to propose some test statistics for testing the skewness parameter of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results indicate that the power of the tests differ significantly across sample sizes, the choice of alternative hypotheses and methods one …

Fitting Skew Distributions To Iranian Auto Insurance Claim Data, Ramin Kazemi, Abdollah Jalilian, Akram Kohansal

Applications and Applied Mathematics: An International Journal (AAM)

In actuary, the derivation of loss distributions from insurance data is of great interest. Fitting an adequate distribution to real insurance data is not an easy task, mainly due to the nature of the data, which shows several features to be accounted for. Although, because of its stochastic and numerical simplicity, it is often assumed that the involved financial risk factors are normally distributed, but empirical studies indicate that most of financial risk factors have distributions with high peaks and heavy tails. Thus, it is important in the actuarial science to model insurance risks with skewed distributions. Claims size data …

Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge

Applications and Applied Mathematics: An International Journal (AAM)

This study presents the reliability assessment of a single unit connected to two types of external supporting devices for its operation. Each type of external supporting device has two copies I and II on standby. First order differential difference equations method is used to obtain the explicit expression for the steady state availability, busy period due to failure of type I and II supporting devices of repairmen, steady-state availability and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and …