Successive maxima of samples from a GEM distribution

2016/09/06 by Pitman, Jim, Yakubovich, Yuri
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1609.01601

Abstract

We show that the maximal value in a size n sample from GEM(θ) distribution is distributed as a sum of independent geometric random variables. This implies that the maximal value grows as θlog(n) as n→∞. For the two-parametric GEM(α,θ) distribution we show that the maximal value grows as a random factor of n^α/(1-α) and find the limiting distribution.

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