Bayesian credible regions for two-parameter exponential distributions under type-II censoring

Abstract

The construction of Bayesian credible sets for two-parameter exponential models under type-II censoring is investigated in this paper. A three-step algorithm to generate samples from the posterior distribution is presented with the aim of determining the highest posterior density (HPD) credible region for the exponential parameters. A two-step procedure is also suggested to find a closed-form Bayesian credible region. Moreover, the HPD credible region for two exponential quantiles is derived using a simulation-based method. The minimum-size frequentist confidence sets for exponential parameters and quantiles numerically coincide with the corresponding Bayesian HPD credible sets when a certain diffuse prior is assumed. A real data example on leukemia remission time data is analyzed for illustration and comparison. Some applications of the proposed Bayesian credible regions are also discussed.