Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

Abstract

In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.