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On Bernoulli trials with unequal harmonic success probabilities

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  • Thierry Huillet

    (CY Cergy Paris University, CNRS UMR-8089 Site de Saint Martin)

  • Martin Möhle

    (Eberhard Karls Universität Tübingen)

Abstract

A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and the time to the first success. Large sample asymptotics, statistical parameter estimation, and relations to Sibuya distributions and Yule–Simon distributions are discussed. This toy model is relevant in several applications including reliability, species sampling problems, record values breaking and random walks with disasters.

Suggested Citation

  • Thierry Huillet & Martin Möhle, 2024. "On Bernoulli trials with unequal harmonic success probabilities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(4), pages 349-378, May.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:4:d:10.1007_s00184-023-00913-5
    DOI: 10.1007/s00184-023-00913-5
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    References listed on IDEAS

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    1. Yamato, Hajime & Sibuya, Masaaki & Nomachi, Toshifumi, 2001. "Ordered sample from two-parameter GEM distribution," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 19-27, November.
    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. Masaaki Sibuya, 2014. "Prediction in Ewens–Pitman sampling formula and random samples from number partitions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 833-864, October.
    4. A. Philippou & G. Roussas, 1975. "Asymptotic normality of the maximum likelihood estimate in the independent not identically distributed case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 45-55, December.
    5. Hong, Yili, 2013. "On computing the distribution function for the Poisson binomial distribution," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 41-51.
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