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

Abstract

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.

Keywords:

• Bayesian prediction
• Exponential distribution
• Markov Chain Monte Carlo
• Order statistics
• Pareto distribution
• Type-I hybrid censored sample

Mathematics Subject Classification:

• Primary 62G30
• Secondary 62F15

Acknowledgments

The authors would like to express their thanks to the referees for their useful comments and suggestions on the original version of this article, which led to this improved version. The second author also acknowledges the support of the National Sciences and Engineering Research Council of Canada and the research grant (Number KSO-VPP-107) from King Saud University, Riyadh, Saudi Arabia, for conducting this research.