Prediction Intervals for Future Order Statistics from a Generalized Modified Weibull

Abstract

Viewing the future order statistics as latent variables at each Gibbs sampling iteration, several Bayesian approaches to predict future order statistics based on type-II censored order statistics, X(1), X(2), …, X(r), of a size n( > r) random sample from a four-parameter generalized modified Weibull (GMW) distribution, are studied. Four parameters of the GMW distribution are first estimated via simulation study. Then various Bayesian approaches, which include the plug-in method, the Monte Carlo method, the Gibbs sampling scheme, and the MCMC procedure, are proposed to develop the prediction intervals of unobserved order statistics. Finally, four type-II censored samples are utilized to investigate the predictions.