Statistics and Probability Commons^™

Mle And Eap Methods For Estimating Ability Scores For Data Of Varying Sample Size And Item Length, Sahar Taji

Graduate Theses and Dissertations

In this research, the performance of two popular estimators, Maximum Likelihood Estimator(MLE) and Bayesian Expected a Posteriori (EAP) is studied and compared in estimating the latent ability score in an Item Response Theory (IRT) model. The 2-Parameter Logistic (2PL) IRT model which is characterized by difficulty and discrimination item parameters is used to estimate the latent ability scores. Several datasets are generated for variety of sample size and item length values. The Monte-Carlo simulation is used to analyze the performance of the estimators. Results show that MLE produces reliable results with low root mean square error (RMSE) across all datasets. …

Bayesian Methods For Graphical Models With Neighborhood Selection., Sagnik Bhadury

Electronic Theses and Dissertations

Graphical models determine associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models, where the relationships are formalized by non-null entries of the precision matrix. However, in high-dimensional cases, covariance estimates are typically unstable. Moreover, it is natural to expect only a few significant associations to be present in many realistic applications. This necessitates the injection of sparsity techniques into the estimation method. Classical frequentist methods, like GLASSO, use penalization techniques for this purpose. Fully Bayesian methods, on the contrary, are slow because they require iteratively sampling over a quadratic …

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Statistical Roles Of The G-Expectation Framework In Model Uncertainty: The Semi-G-Structure As A Stepping Stone, Yifan Li

Electronic Thesis and Dissertation Repository

The G-expectation framework is a generalization of the classical probability system based on the sublinear expectation to deal with phenomena that cannot be described by a single probabilistic model. These phenomena are closely related to the long-existing concern about model uncertainty in statistics. However, the distributions and independence in the G-framework are quite different from the classical setup. These distinctions bring difficulty when applying the idea of this framework to general statistical practice. Therefore, a fundamental and unavoidable problem is how to better understand G-version concepts from a statistical perspective.

To explore this problem, this thesis establishes a new substructure …

Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen

Theses

In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these …

The Q-Analogue Of The Extended Generalized Gamma Distribution, Wenhao Chen

Undergraduate Student Research Internships Conference

This project introduces a flexible univariate probability model referred to as the q-analogue of the Extended Generalized Gamma (or q-EGG) distribution, which encompasses the majority of the most frequently used continuous distributions, including the gamma, Weibull, logistic, type-1 and type-2 beta, Gaussian, Cauchy, Student-t and F. Closed form representations of its moments and cumulative distribution function are provided. Additionally, computational techniques are proposed for determining estimates of its parameters. Both the method of moments and the maximum likelihood approach are utilized. The effect of each parameter is also graphically illustrated. Certain data sets are modeled with q-EGG distributions; goodness of …

To Logit Or Not To Logit Data In The Unit Interval: A Simulation Study, Kayode Idris Hamzat

Major Papers

In this paper, we recommend a mechanism for determining whether to logit or not to logit data in the unit interval which is based on quantile estimation of data between 0 and 1. By using a simulated dataset generated from a Beta regression model, the estimated quantile for this model perform better than those based on the linear quantile regression with logit transformation.

Further, we investigate the performance of the quantile regression estimators based on the LQR and we conclude that it is better than those based on the Beta regression when the distribution is contaminated with 10% uniform numbers …

New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie

Electronic Thesis and Dissertation Repository

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.

The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In …

How Blockchain Solutions Enable Better Decision Making Through Blockchain Analytics, Sammy Ter Haar

Information Systems Undergraduate Honors Theses

Since the founding of computers, data scientists have been able to engineer devices that increase individuals’ opportunities to communicate with each other. In the 1990s, the internet took over with many people not understanding its utility. Flash forward 30 years, and we cannot live without our connection to the internet. The internet of information is what we called early adopters with individuals posting blogs for others to read, this was known as Web 1.0. As we progress, platforms became social allowing individuals in different areas to communicate and engage with each other, this was known as Web 2.0. As Dr. …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

All Dissertations

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

Aberrant Responding With Underlying Dominance And Unfolding Response Processes: Examining Model Fit And Performance Of Person-Fit Statistics, Jennifer A. Reimers

Graduate Theses and Dissertations

Researchers have recognized that respondents may not answer items in a way that accurately reflects their attitude or trait level being measured. The resulting response data that deviates from what would be expected has been shown to have significant effects on the psychometric properties of a scale and analytical results. However, many studies that have investigated the detection of aberrant data and its effects have done so using dominance item response theory (IRT) models. It is unknown whether the impacts of aberrant data and the methodology used to identify aberrant responding when using dominance IRT models apply similarly when scales …

On Misuses Of The Kolmogorov–Smirnov Test For One-Sample Goodness-Of-Fit, Anthony Zeimbekakis

Honors Scholar Theses

The Kolmogorov–Smirnov (KS) test is one of the most popular goodness-of-fit tests for comparing a sample with a hypothesized parametric distribution. Nevertheless, it has often been misused. The standard one-sample KS test applies to independent, continuous data with a hypothesized distribution that is completely specified. It is not uncommon, however, to see in the literature that it was applied to dependent, discrete, or rounded data, with hypothesized distributions containing estimated parameters. For example, it has been "discovered" multiple times that the test is too conservative when the parameters are estimated. We demonstrate misuses of the one-sample KS test in three …

Early-Warning Alert Systems For Financial-Instability Detection: An Hmm-Driven Approach, Xing Gu

Electronic Thesis and Dissertation Repository

Regulators’ early intervention is crucial when the financial system is experiencing difficulties. Financial stability must be preserved to avert banks’ bailouts, which hugely drain government's financial resources. Detecting in advance periods of financial crisis entails the development and customisation of accurate and robust quantitative techniques. The goal of this thesis is to construct automated systems via the interplay of various mathematical and statistical methodologies to signal financial instability episodes in the near-term horizon. These signal alerts could provide regulatory bodies with the capacity to initiate appropriate response that will thwart or at least minimise the occurrence of a financial crisis. …

Parametric And Reliability Estimation Of The Kumaraswamy Generalized Distribution Based On Record Values, Mohd. Arshad, Qazi J. Azhad

Journal of Modern Applied Statistical Methods

A general family of distributions, namely Kumaraswamy generalized family of (Kw-G) distribution, is considered for estimation of the unknown parameters and reliability function based on record data from Kw-G distribution. The maximum likelihood estimators (MLEs) are derived for unknown parameters and reliability function, along with its confidence intervals. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Future record values are predicted using Bayesian approach and non Bayesian approach, based on numerical examples and a monte carlo simulation.

Does The Type Of Records Affect The Estimates Of The Parameters?, Ayush Tripathi, Umesh Singh, Sanjay Kumar Singh

Journal of Modern Applied Statistical Methods

The maximum likelihood estimation of the unknown parameters of inverse Rayleigh and exponential distributions are discussed based on lower and upper records. The aim is to study the effect of the type of records on the behavior of the corresponding estimators. Mean squared errors are calculated through simulation to study the behavior of the estimators. The results shall be of interest to those situations where the data can be obtained in the form of either of the two types of records and the experimenter must decide between these two for estimation of the unknown parameters of the distribution.

Design Of Sksp-R Plan For Popular Statistical Distributions, Jaffer Hussain, S. Balamurali, Muhammad Aslam

Journal of Modern Applied Statistical Methods

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.

Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih

Journal of Modern Applied Statistical Methods

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating …

A New Goodness Of Fit Measure Based On Income Inequality Curves, Shahryar Mirzaei, S. M. A. Jahanshahi

Journal of Modern Applied Statistical Methods

This paper uses inequality-measurement techniques to assess goodness of fit in income distribution models. It exposes the shortcomings of the use of conventional goodness of fit criteria in face of the big income data and proposes a new set of metrics, based on income inequality curves. In this note, we mentioned that the distance between theoretical and empirical inequality curves can be considered as a goodness of fit criterion. We demonstrate certain advantages of this measure over the other general goodness of fit criteria. Unlike other goodness of fit measures, this criterion is bounded. It is 0 in minimum difference …

A Simple Algorithm For Generating A New Two Sample Type-Ii Progressive Censoring With Applications, E. M. Shokr, Rashad Mohamed El-Sagheer, Mahmoud Mansour, H. M. Faied, B. S. El-Desouky

Basic Science Engineering

In this article, we introduce a simple algorithm to generating a new type-II progressive censoring scheme for two samples. It is observed that the proposed algorithm can be applied for any continues probability distribution. Moreover, the description model and necessary assumptions are discussed. In addition, the steps of simple generation algorithm along with programming steps are also constructed on real example. The inference of two Weibull Frechet populations are discussed under the proposed algorithm. Both classical and Bayesian inferential approaches of the distribution parameters are discussed. Furthermore, approximate confidence intervals are constructed based on the asymptotic distribution of the maximum …