Maximizable informational entropy as measure of probabilistic uncertainty

Abstract

In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d<x>-<dx>) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized virtual work principle <dx>=0 leading to maximum entropy d(I-beta*<x>)=0. This paper presents an analytical investigation of this maximizable entropy for several distributions such as stretched exponential distribution, kappa-exponential distribution and Cauchy distribution.