Relationships between cumulative entropy/extropy, Gini mean difference and probability weighted moments

TL;DR

This paper explores the connections between various entropy measures, Gini mean difference, and probability weighted moments, providing new relationships and estimation methods for these statistical measures.

Contribution

It establishes novel links between cumulative residual entropy, extropy, Gini mean difference, and probability weighted moments, enhancing understanding and estimation techniques.

Findings

Established relationships between cumulative residual entropy and Gini mean difference.

Linked entropy and extropy measures to probability weighted moments.

Proposed methods for estimating these entropy measures.

Abstract

In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative extropy are also established. We then show that several entropy and extropy measures discussed here can be brought into the framework of probability weighted moments, which would enable us to find estimators of these measures.