Interval extropy and weighted interval extropy

TL;DR

This paper introduces dynamic measures called Interval Extropy and Weighted Interval Extropy as new ways to quantify uncertainty in doubly truncated random variables, extending the concept of Extropy.

Contribution

It proposes novel dynamic uncertainty measures for truncated variables and explores their properties, transformations, and bounds, expanding the theoretical framework of Extropy.

Findings

Characterizations of random variables related to the new measures

Evaluation of measures under linear transformations

Bounds for Interval Extropy and Weighted Interval Extropy

Abstract

Recently, Extropy was introduced by Lad, Sanfilippo and Agr\`o as a complement dual of Shannon Entropy. In this paper, we propose dynamic versions of Extropy for doubly truncated random variables as measures of uncertainty called Interval Extropy and Weighted Interval Extropy. Some characterizations of random variables related to these new measures are given. Several examples are shown. These measures are evaluated under the effect of linear transformations and, finally, some bounds for them are presented.