Document Type

Thesis

Degree

Master of Science (MS)

Department

Statistics

First Advisor's Name

Hassan Zahedi

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Florence George

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Zhenmin Chen

Third Advisor's Committee Title

Committee Member

Keywords

Failure Rate, Hazard Gradient, Lifetime Distribution, Bivariate Bath-tub Shaped Failure Rate

Date of Defense

10-30-2014

Abstract

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

Identifier

FI14110710

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