On Weighted Extropies

TL;DR

This paper introduces weighted extropy, a shift-dependent information measure emphasizing larger observed values, and extends it to residual, past, and bivariate cases, with illustrative examples.

Contribution

It proposes the novel concept of weighted extropy and its extensions for residual, past, and bivariate cases, expanding the framework of information measures.

Findings

Weighted extropy emphasizes larger values of random variables.

Extensions to residual and past extropies are developed.

Bivariate weighted extropy is introduced.

Abstract

The extropy is a measure of information introduced by Lad et al. (2015) as dual to entropy. As the entropy, it is a shift-independent information measure. We introduce here the notion of weighted extropy, a shift-dependent information measure which gives higher weights to large values of observed random variables. We also study the weighted residual and past extropies as weighted versions of extropy for residual and past lifetimes. Bivariate versions extropy and weighted extropy are also provided. Several examples are presented through out to illustrate the various concepts introduced here.