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

Thierry E. Huillet ()
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Thierry E. Huillet: Laboratoire de Physique Théorique et Modélisation CNRS-UMR 8089 et Université de Cergy-Pontoise

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 321-344

Abstract: 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.

Keywords: Yule-Simon; Sibuya; self-decomposability; Gauss hypergeometric function; urn model; death process with immigration; Markov chain with catastrophes; 60E05 (60E07; 60J10) (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-020-0403-y

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