Bayes Analysis of a Lifetime Model

Abstract

Lifetimes models have been developed in the last five centuries. These developments are purposed to fit lifetimes data. Models that accommodate different shapes of the hazard rate function are useful for analyzing the lifetimes data. Among these lifetimes models is the TN distribution with two parameters. The TN model has variety of shapes for hazard rate function. It accommodates increasing, decreasing, bathtub, unimodal, increasing-decreasing-increasing hazard shapes which allows it to fit variety of real lifetime data sets. The main aim of this thesis is to estimate the two parameters of the TN distribution using the classical and Bayesian methods. In the classical approach, we use the maximum likelihood estimation. While in the Bayesian approach, the rejection sampling algorithm and the Markov Chain Monte Carlo methods are applied to obtain the Bayes estimates of the TN parameters and the tow-sided Bayesian probability intervals of the parameters. Simulation study is performed to investigate the properties of the methods applied and compare the maximum likelihood and the Bayesian methods. In order to demonstrate the use of the methods used in this thesis, three data sets are analyzed using the maximum likelihood and Bayes methods.