Enregistré dans:
Détails bibliographiques
Auteurs principaux: Gnedin, Alexander, Derbazi, Zakaria
Format: Preprint
Publié: 2022
Sujets:
Accès en ligne:https://arxiv.org/abs/2207.05156
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Table des matières:
  • Suppose $N$ independent Bernoulli trials are observed sequentially at random times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. We focus on the version of the problem where the $k^\text{th}$ trial is a success with probability $p_k=θ/(θ+k-1)$ and the prior distribution of $N$ is negative binomial with shape parameter $ν$. Exploring properties of the Gaussian hypergeometric function, we find that the myopic stopping strategy is optimal if and only if $ν\geqθ$. We derive formulas to assess the winning probability and discuss limit forms of the problem for large $N$.