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Kafri, O. (2009) The Distributions in Nature and Entropy Principle. arXiv:0907.4852.

has been cited by the following article:

• TITLE: The Burr XII Distribution Family and the Maximum Entropy Principle: Power-Law Phenomena Are Not Necessarily “Nonextensive”

  AUTHORS: F. Brouers

  KEYWORDS: Buur XII Distribution, Singh-Maddala Distribution, Lévy Function, Entropy, Non-Equilibrium Thermodynamics, Complex Systems, Nonextensivity

  JOURNAL NAME: Open Journal of Statistics, Vol.5 No.7, December 18, 2015

  ABSTRACT: In this paper, we recall for physicists how it is possible using the principle of maximization of the Boltzmann-Shannon entropy to derive the Burr-Singh-Maddala (BurrXII) double power law probability distribution function and its approximations (Pareto, loglogistic.) and extension (GB2…) first used in econometrics. This is possible using a deformation of the power function, as this has been done in complex systems for the exponential function. We give to that distribution a deep stochastic interpretation using the theory of Weron et al. Applied to thermodynamics, the entropy nonextensivity can be accounted for by assuming that the asymptotic exponents are scale dependent. Therefore functions which describe phenomena presenting power-law asymptotic behaviour can be obtained without introducing exotic forms of the entropy.