Bayesian Inference and prediction or order statistics for a Type II censored Weibull distribution

TLDR: In this paper, the authors used Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples and used it to compute the Bayes estimates and also to construct symmetric credible intervals.

Abstract: This paper describes the Bayesian inference and prediction of the two-parameter Weibull distribution when the data are Type-II censored data. The aim of this paper is two fold. First we consider the Bayesian inference of the unknown parameters under different loss functions. The Bayes estimates cannot be obtained in closed form. We use Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples and it has been used to compute the Bayes estimates and also to construct symmetric credible intervals. Further we consider the Bayes prediction of the future order statistics based on the observed sample. We consider the posterior predictive density of the future observations and also construct a predictive interval with a given coverage probability. Monte Carlo simulations are performed to compare different methods and one data analysis is performed for illustration purposes.