{"paper":{"title":"Sampling from a mixture of different groups of coupons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aristides V. Doumas, Vassilis G. Papanicolaou","submitted_at":"2017-09-13T18:45:57Z","abstract_excerpt":"A collector samples coupons with replacement from a pool containing $g$ \\textit{uniform} groups of coupons, where \"uniform group\" means that all coupons in the group are equally likely to occur. For each $j = 1, \\dots, g$ let $T_j$ be the number of trials needed to detect Group $j$, namely to collect all $M_j$ coupons belonging to it at least once. We derive an explicit formula for the probability that the $l$-th group is the first one to be detected (symbolically, $P\\{T_l = \\bigwedge_{j=1}^g T_j\\}$). We also compute the asymptotics of this probability in the case $g=2$ as the number of coupon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04500","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"}