Bayesian Estimation and Prediction of Generalized Pareto Distribution Based on Type II Censored Samples

The study aims to estimate the parameter of the Generalized Pareto Distribution under Type II censored samples. The Bayes Estimators have been derived under a class of informative and non-informative Priors using different symmetric and asymmetric Loss functions. The Credible Intervals, Highest Posterior Density (HPD) intervals, Posterior Predictive Distributions and Posterior Predictive Intervals have been constructed under each Prior. The Bayesian hypothesis testing scheme has also been employed. The performance of the Point and Interval Estimators of the parameter has been evaluated under a simulation study. The findings of the study suggest that in order to have a Point Estimate of the parameter of the Generalized Pareto Distribution under a Bayesian framework, the use of Inverse Gamma Prior along with Entropy Loss Function can be preferred. The Bayesian Interval Estimates and the Posterior Predictive Intervals are also more precise under the assumption of Inverse Gamma Prior.