BAYESIAN ANALYSIS OF SOME RANDOMLY CENSORED LIFETIME DISTRIBUTIONS

Abstract

The thesis presents the Bayesian analysis of some two-parameter lifetime distributions in presence of random censoring. It is well known that for the distributions having shape parameter(s), the conjugate joint prior distributions of shape and scale parameters do not exist while computing the Bayes estimates. In this thesis it is assumed that the shape and scale parameters have independent gamma priors. In case of no prior information about the parameters, the commonly used noninformative priors on the shape and scale parameters are considered. It is observed that the closedform expressions for the Bayes estimators cannot be obtained; four different methods of Bayesian computation are proposed in the crucial places to obtain the approximate Bayes estimates. Among these two are based on analytical approximation, namely, the Lindley’s approximation and the Tierney-Kadane’s approximation; and two are based on Monte Carlo sampling that are importance sampling and Gibbs sampling. For each model, we use three different methods of estimation: maximum likelihood, analytical approximation and Monte Carlo sampling. Simulation studies are carried out to observe the behavior of the Bayes estimators and to compare with the maximum likelihood estimators of the unknown parameters, the hazard function and the reliability function for different sample sizes, different priors, different loss functions, different loss function parameter values and for different censoring rates. The analysis of real data examples is performed in a noble way to illustrate the proposed 10 methodology. Several model fitness measures are taken into consideration to check the goodness-of-fit of the proposed models