New exact Bayesian prediction of the range for the exponential lifetime based on fixed and random sample sizes
We consider the problem of predictive interval for the range of the future observations from an exponential distribution. Two cases are considered, (1) Fixed sample size (FSS). (2) Random sample size (RSS). Further, I derive the predictive function for both FSS and RSS in closely forms. Random sample size is appeared in many application of life testing. Fixed sample size is a special case from the case of random sample size. Illustrative examples are given. Factors of the predictive distribution are given. A comparison in savings is made with the above method. To show the applications of our results, we present some simulation experiments. Finally, we apply our results to some real data sets in life testing.