Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records

Abstract

In this paper, we consider the prediction problem in two-sample case and study the non-parametric predicting future progressively Type-II censored order statistics based on observed $$k$$ k -records from the same distribution. Also, prediction intervals for progressively Type-II censored spacings are obtained based on $$k$$ k -record spacings. It is shown that the coverage probabilities of these intervals are exact and do not depend on the underlying distribution. Moreover, optimal prediction intervals are derived for each case. Finally, for illustrating the proposed procedure, we consider a real data set and numerical computations are given. The results of Ahmadi and Balakrishnan (Statistics 44:417---430, 2010) can be achieved as special cases of our results.