Optimal prediction intervals for random order statistics

In this paper, the problem of predicting future order statistics‎, ‎by assuming the future sample size is a random variable‎, ‎is studied‎. First, a general expression for the coverage probability of the prediction interval is derived‎, when the future sample size has degenerate‎, ‎binomial and Poisson distributions‎. Then, ‎numerical computations are given‎. ‎The procedure for finding an optimal prediction interval is presented for each case‎.