Some Properties of Cumulative Extropy and its Dynamic Past Version

Abstract

Extropy has been discussed in many works of literature as a complementary dual of Shannon’s entropy function. In this paper, a replacement procedure of uncertainty of random variable, constructed on the cumulative distribution function F, called cumulative extropy is proposed. Some properties and features of the deemed measure are
obtained. Moreover, the dynamic form of cumulative extropy is considered. Finally, non-parametric estimators for the proposed measure are included.