BAYESIAN INFERENCE OF THE MIXTURE OF TWO LOMAX DISTRIBUTIONS AS A LIFETIME MODEL

Abstract

The problem of estimation and prediction in reliability and life testing theory has been considered by many authors using both Bayesian and classical approaches for various lifetime distributions and under different types of censoring. Loss functions play an important role in the Bayesian approach. In most of the past literature on mixtures of distributions, problems of estimation were considered under the assumption of the squared error loss function. This thesis deals with Bayesian estimation of the parameters, the reliability function and the hazard rate of the mixture of two Lomax distributions with respect to three symmetric loss functions and two asymmetric ones. A study of the Bayesian estimation assuming the quadratic, the weighted and ElSayyad loss functions is given for the mixture of two Lomax distributions. The linear exponential loss function and the modified linex loss functions are considered as asymmetric loss functions. A comparison between the two types of loss functions is made using the values of the posterior risks and the absolute relative error. Interval Bayesian estimation of the parameters of the mixture of two Lomax distributions is considered. The interim analysis is considered for the mixture of two Lomax distributions as a predictive application on the hypothesis testing. This application can be used to take a decision about continuing in drawing a sample or not. Bayesian predictive intervals for a bivariate Lomax distribution are considered. The one-sample and two-sample prediction are proposed. Numerical examples are provided to illustrate the theoretical work.