On Bernoulli trials with unequal harmonic success probabilities

Thierry Huillet () and Martin Möhle ()
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Thierry Huillet: CY Cergy Paris University, CNRS UMR-8089 Site de Saint Martin
Martin Möhle: Eberhard Karls Universität Tübingen

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 4, No 1, 349-378

Abstract: 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.

Keywords: Bernoulli variables; Ewens–Pitman sampling formula; Markov chains; Rényi’s records; Sibuya distribution; Stirling numbers; Yule–Simon distribution; Primary 60J10; Secondary 60C05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00913-5

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