On extropy of past lifetime distribution

TL;DR

This paper introduces the concept of past extropy as a new measure of uncertainty in past lifetime distributions, extending the idea of residual extropy, and explores its properties and applications.

Contribution

It defines and analyzes past extropy, a novel measure of uncertainty for past lifetime distributions, and provides a characterization of its behavior for largest order statistics.

Findings

Past extropy effectively measures uncertainty in past lifetime data.

Characterization results for largest order statistics.

Connections between past and residual extropy established.

Abstract

Recently Qiu et al. (2017) have introduced residual extropy as measure of uncertainty in residual lifetime distributions analogues to residual entropy (1996). Also, they obtained some properties and applications of that. In this paper, we study the extropy to measure the uncertainty in a past lifetime distribution. This measure of uncertainty is called past extropy. Also it is showed a characterization result about the past extropy of largest order statistics.