One- and Two-Sample Bayesian Prediction Intervals Based on Type-I Hybrid Censored Data

In this article, we consider a general form for the underlying distribution and a general conjugate prior, and describe a general procedure for determining the Bayesian prediction intervals for future lifetimes based on an observed Type-I hybrid censored data. For the illustration of the developed results, the Exponential(θ) and Pareto(α, β) distributions are used as examples. One-sample Bayesian predictive survival function can not be obtained in closed-form and so Gibbs sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which are then used to compute the approximate predictive survival function. Finally, some numerical results are presented to illustrate all the inferential results developed here.