Varentropy of past lifetimes

TL;DR

This paper introduces a new concept of varentropy for past lifetime distributions, exploring its properties, relationships with past entropy, and effects of transformations, with applications to proportional reversed hazard models.

Contribution

It defines and analyzes a novel varentropy measure for past lifetimes, extending reliability theory and connecting it with existing entropy concepts.

Findings

Past varentropy is related to past entropy and other reliability measures.

Linear and monotonic transformations affect past varentropy in specific ways.

Explicit evaluation of past varentropy for proportional reversed hazard models.

Abstract

In Reliability Theory, uncertainty is measured by the Shannon entropy. Recently, in order to analyze the variability of such measure, varentropy has been introduced and studied. In this paper we define a new concept of varentropy for past lifetime distributions as the variability of uncertainty in past lifetime. We analyze the relation of this varentropy with the corresponding past entropy and other concepts of interest in reliability and we study the effect of linear and monotonic transformations on it. Finally, we evaluate past varentropy for random variables following a proportional reversed hazard rate model.