{"paper":{"title":"Mutual information of Contingency Tables and Related Inequalities","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Peter Harremo\\\"es","submitted_at":"2014-02-01T15:28:20Z","abstract_excerpt":"For testing independence it is very popular to use either the $\\chi^{2}$-statistic or $G^{2}$-statistics (mutual information). Asymptotically both are $\\chi^{2}$-distributed so an obvious question is which of the two statistics that has a distribution that is closest to the $\\chi^{2}$-distribution. Surprisingly the distribution of mutual information is much better approximated by a $\\chi^{2}$-distribution than the $\\chi^{2}$-statistic. For technical reasons we shall focus on the simplest case with one degree of freedom. We introduce the signed log-likelihood and demonstrate that its distributi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0092","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"}