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On New Mechanisms Leading to Heavy-Tailed Distributions Related to the Ones Of Yule-Simon

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  • Thierry E. Huillet

    (Laboratoire de Physique Théorique et Modélisation CNRS-UMR 8089 et Université de Cergy-Pontoise)

Abstract

Scientists reinvent stochastic mechanisms leading to the emergence of a distribution discovered by H.A. Simon, in the context of the study of word frequencies occurring in a textbook. Simon distributions are heavy-tailed as a result of a reinforcement mechanism that produced them, related to the modern notion of preferential attachment. The Simon distribution is a particular case of a distribution recently introduced, itself extending the Sibuya distribution. We exhibit some of the remarkable statistical properties of such a family of distributions, in particular the one of being discrete self-decomposable. Using this and after placing this problem in context, additional stochastic processes where such distributions naturally arise are investigated, in particular a Markov chain model with catastrophes.

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  • Thierry E. Huillet, 2020. "On New Mechanisms Leading to Heavy-Tailed Distributions Related to the Ones Of Yule-Simon," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 321-344, March.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0403-y
    DOI: 10.1007/s13226-020-0403-y
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    1. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "A generalized Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 855-887, August.
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    4. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
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    1. Thierry E. Huillet, 2022. "Chance Mechanisms Involving Sibuya Distribution and its Relatives," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 722-764, November.

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