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On Bernoulli trials with unequal harmonic success probabilities

Author

Listed:
  • 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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