On the stability of analytic entropic forms

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]=Sigma(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 Sigma(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. (C) 2003 Elsevier B.V. All rights reserved.