A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians

J.-F. Bercher

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 19, 4460-4469

Abstract: We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The Rényi divergence appears as a natural by-product of the setting. We study the dynamics of the Fisher information on this path, and show in particular that the thermodynamic divergence is proportional to Jeffreys’ divergence. Next, we consider the problem of inferring a distribution on the escort-path, subject to generalized moment constraints. We show that our setting naturally induces a rationale for the minimization of the Rényi information divergence. Then, we derive the optimum distribution as a generalized q-Gaussian distribution.

Keywords: Divergence measures; Generalized Rényi and Tsallis entropies; Escort distributions; q-Gaussian distributions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:19:p:4460-4469

DOI: 10.1016/j.physa.2012.04.024

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