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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2207.05156 |
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| _version_ | 1866917809192173568 |
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| author | Gnedin, Alexander Derbazi, Zakaria |
| author_facet | Gnedin, Alexander Derbazi, Zakaria |
| contents | 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 $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Last-Success Stopping Problem with Random Observation Times Gnedin, Alexander Derbazi, Zakaria Probability 60G40 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 $N$. |
| title | The Last-Success Stopping Problem with Random Observation Times |
| topic | Probability 60G40 |
| url | https://arxiv.org/abs/2207.05156 |