الفهرس 
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Abstract
Inference problems concerning any parameter or set of parameters � can
be easily dealt with using Bayesian analysis. The idea is that since the
posterior distribution supposedly contains all the available information
about � (both sample and prior information) any inferences concerning �
should consists solely of features of this distribution. The simplest
inferential use of the posterior distribution is to report a point estimate for
� with an associate measure of accuracy.
In all but very stylized problems, the integrals required for Bayesian
computation require analytic or numerical approximation. These include asymptotic approximations,
numerical integrations and Monte Carlo importance sampling. The method that we shall use in this
thesis is the Monte Carlo methods, which estimate features of the posterior or predictive
distribution of interest by using samples drawn from that distribution, or suitably reweighted
samples drawn from some other appropriately chosen distribution. Often, particularly in high
dimensional problems, this may be only feasible approach.
In section (1) of this chapter, we define the generalized exponential distribution (GED) and some
of its properties with a review of literature. Some basic concepts of finite mixture, maximum
likelihood, reliability, order statistics, complete and censored data sets, Bayesian prediction and
others are given in section (2). Finally, our aim of this thesis and a description to the problem
of study is presented in section (3).
1. Generalized exponential distribution (GED)
In this thesis we consider a population with density given by a mixture of two components each a
generalized exponential distribution. Inferences about the parameters of this mixture are discussed
under different types of