{"paper":{"title":"Local Limit Theorems for Poisson's Binomial in the Case of Infinite Expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Italo Simonelli, Lucia D. Simonelli","submitted_at":"2018-03-12T08:36:15Z","abstract_excerpt":"Let $ V_{n} = X_{1,n} + X_{2,n} + \\cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\\lambda_{n} = \\sum\\limits_{i=1}^{n} b(i;n) $, $\\lambda = \\lim\\limits_{n \\to \\infty} \\lambda_n,$ and $m_n = \\max\\limits_{1 \\leq i \\leq n} b(i;n)$. We derive asymptotic results for $P(V_{n}=k)$ that hold without assuming that $\\lambda < +\\infty$ or $m_n \\to 0$. Also, we do not assume $k$ to be fixed, but instead, our results hold uniformly for all $k$ which satisfy particular growth conditions with respect to $n$. These results extend known P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04153","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"}