Real and spurious contributions for the Shannon, Renyi and Tsallis entropies

A two-parameter probability distribution is constructed by dilatation (or contraction) of the escort probability distribution. This transformation involves a physical probability distribution P associated with the system under study and an almost arbitrary reference probability distribution P'. In contrast to the Shannon and Renyi entropies, the Tsallis entropy does not decompose as the sum of the physical contribution due to P and the reference or spurious part owing to P'. For solving this problem, a slight modification to the relation between Tsallis and Renyi entropies must be introduced. The procedure in this paper gives rise to a nonconventional one-parameter Shannon entropy and to two-parameter Renyi and Tsallis entropies associated with P. It also contributes to clarify the meaning and role of the escort probabilities set. (C) 2010 Elsevier B.V. All rights reserved.