Bayesian Inference Based on type-I Hybrid Censored Data from a Two-Parameter Exponential Distribution

A hybrid censoring is a mixture of type-I and type-II censoring schemes. It is categorized to type-I and type-II hybrid censored based on how the experiment set to terminate. In this paper, we describe the type-I hybrid censoring where lifetime variables have a two-parameters exponential distribution. Bayes estimation of unknown parameters under squared error loss function is developed. Among several methods of constructing the optimal procedures in the context of robust Bayesian methodology, we obtain posterior regret gamma minimax estimation of unknown parameters under squared error loss function. Finally, we discuss minimaxity and admissibility of the generalized Bayes estimator under squared error loss.