Comparison among non parametric prediction intervals of order statistics

Abstract

In this article, we are interested in conducting a comparison study between different non parametric prediction intervals of order statistics from a future sample based on an observed order statistics. Typically, coverage probabilities of well-known non parametric prediction intervals may not reach the preassigned probability levels. Moreover, prediction intervals for predicting future order statistics are no longer available in some cases. For this, we propose different methods involving random indices and fractional order statistics. In each case, we find the optimal prediction intervals. Numerical computations are presented to assess the performances of the so-obtained intervals. Finally, a real-life data set is presented and analyzed for illustrative purposes.