{"paper":{"title":"On closeness of two discrete weighted sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Palaniappan Vellaisamy, Vydas \\v{C}ekanavi\\v{c}ius","submitted_at":"2018-06-11T07:45:20Z","abstract_excerpt":"The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\\cdots+w_NS_N$ is investigated. Here, $S_i$'s are sums of integer-valued random variables, and $w_i$ denote weights, $i=1,\\dots,N$. Two cases are considered: the general case of independent random variables when their closeness is ensured by the matching of factorial moments and the case when the $S_i$ has the Markov Binomial distribution. The Kolmogorov metric is used to estimate the accuracy of approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03844","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":""},"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"}