Bayesian Inference and Prediction using Progressive First-Failure Censored from Generalized Pareto Distribution

Abstract

This paper describes the Bayesian inference and prediction of the generalized Pareto (GP) distribution for progressive first- failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chian Monte Carlo (MCMC) samples, and theyhave in turn, been used to compute the Bayes estimates with the help of importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two sample Bayes prediction to predicting future order statistics and upper record values from generalized Pareto (GP) distribution based on progressive first-failure censored data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics and upper record values. A simulated data set is used to illustrate the results derived.