On Bernoulli Trials with unequal harmonic success probability.

Resumen:  A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some if 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, parameter estimation, and relations to Sibuya distributions and Yule–Simon distributions are briefly discussed. Stirling numbers play a key role in the analysis. This toy model is relevant in several applications including reliability, species sampling problems, record values breaking and random walks with disasters.

Posted on Apr 22, 2024 in Seminario de Probabilidades de Chile, Seminars