{"paper":{"title":"On the recent-$k$-record of discrete random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anshui Li","submitted_at":"2022-08-14T06:29:09Z","abstract_excerpt":"Let $X_1,~X_2,\\cdots$ be a sequence of i.i.d random variables which are supposed to be observed in sequence. The $n$th value in the sequence is a $k-record~value$ if exactly $k$ of the first $n$ values (including $X_n$) are at least as large as it. Let ${\\bf R}_k$ denote the ordered set of $k$-record values. The famous Ignatov's Theorem states that the random sets ${\\bf R}_k(k=1,2,\\cdots)$ are independent with common distribution. We introduce one new record named $recent-k-record$ (RkR in short) in this paper: $X_n$ is a $j$-RkR if there are exactly $j$ values at least as large as $X_n$ in $X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.06791","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.06791/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}