Bayesian Inference and Prediction of Order Statistics for a Type-II Censored Weibull Distribution Debasis Kundu 1,∗ and Mohammad Z. Raqab 2,∗ 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 witha given coverage probability. Monte Carlo simulations are performed to compare different methods and one data analysis is performed for illustration purposes. Key Words and Phrases: Bayes estimates; Asymptotic distribution; Type-II censoring; Markov Chain Monte Carlo; Predictive density. Address of correspondence: Debasis Kundu, e-mail: kundu@iitk.ac.in, Phone no. 91- 512-2597141, Fax no. 91-512-2597500. 1 Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Pin 208016, India. Visiting Professor at King Saud University. 2 Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia. * The authors would like to thank the deanship of scientific research at King Saud University and department of science and technology of government of India for supporting this research project. 1