{"paper":{"title":"Entropy and the Law of Small Numbers","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ioannis Kontoyiannis, Oliver Johnson, Peter Harremoes","submitted_at":"2002-11-01T17:21:52Z","abstract_excerpt":"Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\\sum_{i=1}^nX_i$ is the sum of the (possibly dependent) binary random variables $X_1,X_2,...,X_n$, with $E(X_i)=p_i$ and $E(S_n)=\\la$, then \\ben D(P_{S_n}\\|\\Pol)\\leq \\sum_{i=1}^n p_i^2 + \\Big[\\sum_{i=1}^nH(X_i) - H(X_1,X_2,..., X_n)\\Big], \\een where $D(P_{S_n}\\|{Po}(\\la))$ is the relative entropy between the distribution of $S_n$ and the Poisson($\\la$) distribution. The first term in this bound measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211020","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"}