Optimal Prediction Intervals for Future Order Statistics from Extreme Value Distributions

摘要

Prediction intervals for future order statistics are widely used for reliability problems and other related problems. The determination of these intervals has been extensively investigated. But the optimality property of these intervals has not been fully explored. In this paper we discuss this problem for extreme value distributions. Introducing a risk function to compare prediction intervals, the interval which minimizes it among the class of invariant prediction intervals is obtained. The technique used here for optimization of prediction intervals based on censored data emphasizes pivotal quantities relevant for obtaining ancillary statistics and factors. It allows one to solve the optimization problems in a simple way.