Exact prediction intervals for exponential lifetime based on random sample size

In this paper, we generalize the work by Lawless (1971) and Lingappaiah (1973) for predicting future order statistics from exponential lifetime when the sample size is a random variable. First, we derive the distributions of some pivotal quantities that can be used to predict future order statistics from exponential lifetime when the sample size is Poisson and binomial distributed. Next, we calculate the percentage points (factors) of the predictive distributions and use them to construct predictive confidence intervals for the future order statistics. To show the usefulness of our results, we present some simulation experiments. Finally, we apply our techniques to some real data sets in life testing.