Exact prediction intervals for future exponential lifetime based on random generalized order statistics

In this paper we develop two pivotal quantities to construct exact predication intervals for future exponential lifetime based on a random number of lower generalized order statistics. The distribution functions of the two pivotal quantities, when the sample size is assumed to be integer‐valued random variable, are derived. Three important special cases for the random sample size are presented. A simulation study is conducted for illustrative purposes.