Award Date

May 2023

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Malwane Ananda

Second Committee Member

Amei Amei

Third Committee Member

Hokwon Cho

Fourth Committee Member

Qing Wu

Number of Pages

136

Abstract

The concept of composite distributions was proposed in the early 2000s as a good parametric solution to model the data with heavy tails. Since the concept was proposed, it has been widely used in different areas, such as modeling insurance claim size data, predicting the risk measures in insurance data analysis, fitting survival time data, and modeling precipitation data. While a lot of the composite distributions demonstrated great performances in real applications, many commonly used composite distributions such as the inverse gamma-Pareto (IGP) or exponential-Pareto (EP), did not demonstrate great performances when fitting to several particular data sets. In order to improve the performance of the original composite distributions, a generalized family of exponentiated composite distributions (GEC) is proposed by adding an extra parameter. Some important mathematical properties of this family of models are derived. For real applications, the exponentiated inverse gamma-Pareto (EIGP) and the exponentiated exponential-Pareto distributions (EEP) were developed as two special models from this family. The properties of these two models are discussed. The parameter estimation procedures of these two models are described with extensive simulations. The Goodness-of-Fit tests of these two models were also presented with simulations. For the real data applications, several widely-used insurance, survival, and reliability data sets were chosen, and it was demonstrated that both models can provide great fitting performances when fitting to different types of data sets. The success of these two special models from the family suggests that other models from the family may also have great potential in modeling the right-skewed data with very heavy tails.

Keywords

composite distribution; exponentiated model; insurance data modeling; positively skewed data modeling; reliability data modeling; survival data modeling

Disciplines

Statistics and Probability

File Format

pdf

Degree Grantor

University of Nevada, Las Vegas

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

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