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

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 moments 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.
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Physica A: Statistical Mechanics and its Applications, Elsevier, 2012, 391 (19), pp.4460-4469. <10.1016/j.physa.2012.04.024>
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Contributeur : Jean-François Bercher <>
Soumis le : mercredi 19 septembre 2012 - 14:22:17
Dernière modification le : mercredi 19 septembre 2012 - 15:55:41

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Jean-François Bercher. A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians. Physica A: Statistical Mechanics and its Applications, Elsevier, 2012, 391 (19), pp.4460-4469. <10.1016/j.physa.2012.04.024>. <hal-00733755>

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