Date of Award

1-6-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Science

First Advisor

Hassan Elsalloukh

Abstract

The Epsilon Skew Exponential Power Distribution (ESEP) that was introduced by Elsalloukh et al. (2005) is an asymmetric distribution used for modeling asymmetric data. The ESEP includes Normal, Laplace, Epsilon Skew Normal (ESN), and Epsilon Skew Laplace (ESL) as particular cases, Elsalloukh et al. (2005). In the present study, since the ESEP distribution encompasses members with skewed and symmetric distributions, we perform and investigate the Bayesian analysis of this distribution using the methods of latent variables and uniform scale mixture for implementing the most common Markov chain Monte Carlo (MCMC) algorithm known as Gibbs sampling. Furthermore, we develop the posterior distributions and the full conditional distributions of each parameter of the ESEP using Jeffrey's non-informative and informative priors for each parameter. We generate observations using the uniform scale mixture from the ESEP and develop a Gibbs sampling algorithm which helps to generate the posterior of each parameter. We compare the ESEP to other asymmetric distributions using the most common comparison technique Deviance Information Criteria (DIC). Finally, we derive a multivariate version, the Multivariate Epsilon Skew Exponential Power Distribution (MESEP), of the ESEP distribution. We then study its properties and derive its central moments, mean, variance, and maximum likelihood estimation. We also derive distributions in special cases of the MESEP distribution. We simulate observations from the bivariate random variables. Finally, we provide examples and applications to show the fitting accuracy and strength of the ESEP and MESEP distribution compared to other distributions used in literature.

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