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

Diógenes Campos

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 18, 3761-3768

Abstract: 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 Rényi 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 Rényi entropies must be introduced. The procedure in this paper gives rise to a nonconventional one-parameter Shannon entropy and to two-parameter Rényi and Tsallis entropies associated with P. It also contributes to clarify the meaning and role of the escort probabilities set.

Keywords: Rényi entropy; Tsallis entropy; Shannon entropy; Incomplete normalization; Overcomplete normalization; Escort probabilities (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:18:p:3761-3768

DOI: 10.1016/j.physa.2010.05.029

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