Bayesian inference for the reliability of generalized inverted exponential distribution under progressive type-I interval censoring

In this paper, we consider the maximum likelihood (ML) and the Bayesian estimators of the parameters, reliability and hazard functions for the generalized inverted exponential distribution under progressive type-I interval censoring. We propose EM algorithm to obtain the ML estimators. The asymptotic confidence intervals are constructed based on the ML estimators. In order to construct the asymptotic confidence intervals of the reliability and hazard functions, we compute variances of them by using delta method. It is observed that the closed-form expressions for the Bayesian estimates cannot be obtained. So we use Tierney-Kadane's approximation and Gibbs sampling method to obtain these estimates. We also derive the Bayesian credible intervals by using Gibbs sampling. Monte-Carlo simulation study is performed to compare the performances of the proposed methods concerning different sample sizes and censoring schemes. Finally, a real data set is analyzed for illustrative purposes.