Successive maxima of samples from a GEM distribution
| Autor: | Pitman, Jim, Yakubovich, Yuri |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that the maximal value in a size $n$ sample from GEM$(\theta)$ distribution is distributed as a sum of independent geometric random variables. This implies that the maximal value grows as $\theta\log(n)$ as $n\to\infty$. For the two-parametric GEM$(\alpha,\theta)$ distribution we show that the maximal value grows as a random factor of $n^{\alpha/(1-\alpha)}$ and find the limiting distribution. Comment: 10 pages |
| Databáze: | arXiv |
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