{"paper":{"title":"Finite sample properties of the mean occupancy counts and probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Geoffrey Decrouez, Michael Grabchak, Quentin Paris","submitted_at":"2016-01-25T10:00:30Z","abstract_excerpt":"For a probability distribution $P$ on an at most countable alphabet $\\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\\mathbb E K_{n,r}$ and probabilities $\\mathbb E M_{n,r}$. Both upper and lower bounds are given in terms of the counting function $\\nu$ of $P$. Special attention is given to the case where $\\nu$ is bounded by a regularly varying function. In this case, it is shown that our general results lead to an optimal-rate control of the expected occupancy counts and probabilities with explicit constants. Our results are also put in perspective with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06537","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"}