  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.
