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Chance Mechanisms Involving Sibuya Distribution and its Relatives

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  • Thierry E. Huillet

    (CY Cergy Paris Université)

Abstract

The two-parameters generalized Sibuya discrete distributions capture the essence of random phenomena presenting large probability mass near the lower bound of its support balanced with heavy-tails in their deep upper bound. They are heavy-tailed as a result of the reinforcement mechanism that produced them, related to the modern notion of preferential attachment. We describe stochastic mechanisms (chiefly Markov chains) leading to the emergence of such distributions, starting with the particular case of the one-parameter Simon distribution appearing in the context of word frequencies occurring in a textbook. We exhibit some of the remarkable statistical properties of the generalized Sibuya distributions. A second related two-parameters Sibuya family is investigated in the same spirit: the class of scaled Sibuya distributions.

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  • 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.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00282-5
    DOI: 10.1007/s13571-022-00282-5
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    1. Pillai, R. N. & Jayakumar, K., 1995. "Discrete Mittag-Leffler distributions," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 271-274, May.
    2. 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.
    3. Holger Dette & James Allen Fill & Jim Pitman & William J. Studden, 1997. "Wall and Siegmund Duality Relations for Birth and Death Chains with Reflecting Barrier," Journal of Theoretical Probability, Springer, vol. 10(2), pages 349-374, April.
    4. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    5. 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.
    6. 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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