Failure extropy, dynamic failure extropy and their weighted versions

TL;DR

This paper introduces failure extropy and its dynamic and weighted variants, exploring their properties, unique characterization, and proposing nonparametric estimators, expanding the theoretical framework of entropy measures.

Contribution

It presents the first comprehensive study of failure extropy, including dynamic and weighted versions, with theoretical properties and nonparametric estimation methods.

Findings

Dynamic failure extropy uniquely characterizes distribution functions.

Weighted measures have advantageous properties.

Nonparametric estimators are developed based on empirical distribution functions.

Abstract

Extropy was introduced as a dual complement of the Shannon entropy. In this investigation, we consider failure extropy and its dynamic version. Various basic properties of these measures are presented. It is shown that the dynamic failure extropy characterizes the distribution function uniquely. We also consider weighted versions of these measures. Several virtues of the weighted measures are explored. Finally, nonparametric estimators are introduced based on the empirical distribution function.