Measures of inaccuracy based on Varextropy

TL;DR

This paper introduces new measures of inaccuracy and discrimination based on varextropy, providing theoretical properties, bounds, and applications in distribution comparison and goodness-of-fit assessment.

Contribution

It derives the generating function of extropy, proposes new varextropy-based inaccuracy measures, and introduces a discrimination measure for distribution comparison.

Findings

Derived the generating function of extropy.

Proposed and analyzed new varextropy-based inaccuracy measures.

Compared the discrimination measure with Kullback-Leibler divergence-based dispersion index.

Abstract

Recently, varextropy has been introduced as a new dispersion index and a measure of information. In this article, we derive the generating function of extropy and present its infinite series representation. Furthermore, we propose new variability measures: the inaccuracy and weighted inaccuracy measures between two random variables based on varextropy and we investigate their properties. We also obtain lower bounds for the inaccuracy measure and compare them with each other. In addition, we introduce a discrimination measure based on varextropy and employ it both for comparing probability distributions and for assessing the goodness of fit of distributions to data and we compare this measure with the dispersion index derived from the Kullback-Leibler divergence given in Balakrishnan et al. (2022).