Measures of uncertainty are a topic of considerable and growing interest. Recently, the introduction of extropy as a measure of uncertainty, dual to Shannon entropy, has opened up interest in new aspects of the subject. Since there are many versions of entropy, a unified formulation has been introduced to work with all of them in an easy way. Here we consider the possibility of defining a unified formulation for extropy by introducing a measure depending on two parameters. For particular choices of parameters, this measure provides the well-known formulations of extropy. Moreover, the unified formulation of extropy is also analyzed in the context of the Dempster–Shafer theory of evidence, and an application to classification problems is given.

This paper concentrates on the fundamental concepts of entropy, information and divergence to the case where the distribution function and the respective survival function play the central role in their definition. The main aim is to provide an overview of these three categories of measures of information and their cumulative and survival counterparts. It also aims to introduce and discuss Csiszár's type cumulative and survival divergences and the analogous Fisher's type information on the basis of cumulative and survival functions.