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
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methodology. Several model fitness measures are taken into consideration to check
the goodness-of-fit of the proposed models
