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A generalized Sibuya distribution

Author

Listed:
  • Tomasz J. Kozubowski

    (University of Nevada)

  • Krzysztof Podgórski

    (Lund University)

Abstract

The Sibuya distribution arises as the distribution of the waiting time for the first success in Bernoulli trials, where the probabilities of success are inversely proportional to the number of a trial. We study a generalization that can be viewed as the distribution of the excess random variable $$N-k$$ N - k given $$N>k$$ N > k , where N has the Sibuya distribution and k is an integer. We summarize basic facts regarding this distribution and provide several new results and characterizations, shedding more light on its origin and possible applications. In particular, we emphasize the role Sibuya distribution plays in the extreme value theory and point out its invariance property with respect to random thinning operation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:4:d:10.1007_s10463-017-0611-3
    DOI: 10.1007/s10463-017-0611-3
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    References listed on IDEAS

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    Cited by:

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    3. Peter Kern & Svenja Lage, 2023. "On Self-Similar Bernstein Functions and Corresponding Generalized Fractional Derivatives," Journal of Theoretical Probability, Springer, vol. 36(1), pages 348-371, March.
    4. Thomas M. Michelitsch & Federico Polito & Alejandro P. Riascos, 2023. "Semi-Markovian Discrete-Time Telegraph Process with Generalized Sibuya Waiting Times," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    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. Balakrishnan, N. & Jones, M.C., 2022. "Closure of beta and Dirichlet distributions under discrete mixing," Statistics & Probability Letters, Elsevier, vol. 188(C).

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