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

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  • Bercher, J.-F.

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.

Suggested Citation

  • Bercher, J.-F., 2012. "A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4460-4469.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:19:p:4460-4469
    DOI: 10.1016/j.physa.2012.04.024
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    References listed on IDEAS

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    1. Pennini, F. & Plastino, A.R. & Plastino, A., 1998. "Rènyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(3), pages 446-457.
    2. Pennini, F. & Plastino, A. & Ferri, G.L., 2007. "Semiclassical information from deformed and escort information measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 782-796.
    3. V. Schwämmle & F. D. Nobre & C. Tsallis, 2008. "q-Gaussians in the porous-medium equation: stability and time evolution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(4), pages 537-546, December.
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    Cited by:

    1. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2018. "Optimal hazard models based on partial information," European Journal of Operational Research, Elsevier, vol. 270(2), pages 723-733.
    2. Puertas-Centeno, D., 2019. "Differential-escort transformations and the monotonicity of the LMC-Rényi complexity measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 177-189.
    3. Kharazmi, Omid & Balakrishnan, Narayanaswamy, 2021. "Jensen-information generating function and its connections to some well-known information measures," Statistics & Probability Letters, Elsevier, vol. 170(C).

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