Measures of inaccuracy based on Varextropy

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 model selection problems. The proposed measure is also compared with the dispersion index derived from the Kullback-Leibler divergence given in Balakrishnan et al. (2024).