Term of Award

Spring 2013

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematical Sciences

Committee Chair

Broderick O. Oluyede

Committee Member 1

Charles Champ

Committee Member 2

Hani Samawi

Abstract

In this thesis, some fundamental results on the weighted and parent FellerPareto and related distributions are presented. Moments, measures of uncertainty including Shannon and s-entropies are presented. Some applications are given. We also introduce the Kumaraswamy distribution and the class of generalized Pareto distributions, and presents results on a more flexible and generalized class of distributions called the Kumaraswamy generalized Pareto class of distributions. Pareto type distributions are flexible parametric models with applications in reliability, actuarial science, economics, finance and telecommunications. We study some mathematical and statistical properties of the Kumaraswamy generalized Pareto distribution including the hazard function, reverse hazard function and moments with particular emphasis on the class of generalized Pareto sub-models.

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