{"paper":{"title":"Ordered and size-biased frequencies in GEM and Gibbs models for species sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jim Pitman, Yuri Yakubovich","submitted_at":"2017-04-16T07:34:06Z","abstract_excerpt":"We describe the distribution of frequencies ordered by sample values in a random sample of size $n$ from the two parameter GEM$(\\alpha,\\theta)$ random discrete distribution on the positive integers. These frequencies are a $($size$-\\alpha)$-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well known identity in distribution due to Donnelly and Tavar\\'e (1986) for $\\alpha = 0$ to the case $0 \\le \\alpha < 1$. This description extends to sampling from Gibbs$(\\alpha)$ frequencies obtained"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04732","kind":"arxiv","version":2},"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"}