Varentropy of past lifetimes

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.