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

Keywords:

Prediction interval , Random sample size , Complete beta function