Weighted extropy for residual life based on Order Statistics

Abstract

In this paper, we discuss novel discoveries regarding the weighted residual extropy of random events. We specifically investigate the weighted extropy of the i-th order statistic and its connection to the weighted residual extropy of the i-th order statistic derived from a random sample following a uniform distribution.
Also, we explore some characterization results, monotone properties and bounds of weighted residual extropy of order statistics. Furthermore, we examine the monotonic tendencies of the weighted residual extropy in order statistics. Non-parametric estimations of the proposed measures based on the kernel and empirical estimators are discovered and by using some simulation studies, the efficiency of them are compared based on their bias and mean square error. Finally, we give a real example to show the usefulness of the proposed estimators for the problem of goodness-of-fit test.