On the stability of analytic entropic forms

Abstract

The stability against small perturbations on the probability distributions (also called experimental robustness) of analytic entropic forms is analyzed. Entropies S[ p], associated with a given set of probabilities { p i }, that can be written in the simple form S[p]=∑ i=1 W r(p i) , are shown to be robust, if r( p i ) is an analytic function of the p i 's. The same property holds for entropies Σ( S[ p]) that are monotonic and analytic functions of S[ p]. The Tsallis entropy S q [ p] falls in the first class of entropies, whenever the entropic index q is an integer greater than 1. A new kind of entropy, that follows such requirements, is discussed.