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arXiv · 1609.01601

Successive maxima of samples from a GEM distribution

Jim Pitman·Yuri Yakubovich
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Abstract

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.

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Jim Pitman, Yuri Yakubovich. 2016-09-06. Successive maxima of samples from a GEM distribution. https://arxiv.org/abs/1609.01601

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