{"paper":{"title":"Successive maxima of samples from a GEM distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jim Pitman, Yuri Yakubovich","submitted_at":"2016-09-06T15:22:35Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01601","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}