Exact Bayesian prediction of exponential lifetime based on fixed and random sample sizes

Abstract

We consider the problem of predictive intervals for future observations from an exponential distribution. We consider the following two cases: (i) fixed sample size (FSS), and (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation examples. Finally, we apply our results to some real data sets in life testing given in Lawless [16].