On Bernoulli trials with unequal harmonic success probabilities. (English) Zbl 07846502

Huillet, Thierry; Möhle, Martin

Metrika 87, No. 4, 349-378 (2024).

Authors’ 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.

Reviewer: Alexander I. Zejfman (Vologda)

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60C05	Combinatorial probability

Keywords:

Bernoulli variables; Ewens-Pitman sampling formula; Markov chains; Rényi’s records; Sibuya distribution; Stirling numbers; Yule-Simon distribution

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