Distribution-free prediction intervals for order statistics based on record coverage

Abstract

In this paper, based on the largest and smallest observations at the times when a new record<br><br>of either kind (upper or lower) occurs, we discuss the prediction of future order statistics.<br><br>The proposed prediction intervals are distribution-free in that the corresponding coverage<br><br>probabilities are known exactly without any assumption about the parent distribution<br><br>other than that it being continuous. An exact expression for the prediction coefficient<br><br>of these intervals is derived. Similarly, prediction intervals for future records based on<br><br>observed order statistics are also obtained. Finally, two real-life data, one involving the<br><br>average July temperatures in Neurenburg, Switzerland, and the other involving the amount<br><br>of annual rainfall at the Los Angeles Civic Center, are used to illustrate the procedures<br><br>developed here.