{"paper":{"title":"Relative log-concavity and a pair of triangle inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yaming Yu","submitted_at":"2010-10-11T09:09:53Z","abstract_excerpt":"The relative log-concavity ordering $\\leq_{\\mathrm{lc}}$ between probability mass functions (pmf's) on non-negative integers is studied. Given three pmf's $f,g,h$ that satisfy $f\\leq_{\\mathrm{lc}}g\\leq_{\\mathrm{lc}}h$, we present a pair of (reverse) triangle inequalities: if $\\sum_iif_i=\\sum_iig_i<\\infty,$ then \\[D(f|h)\\geq D(f|g)+D(g|h)\\] and if $\\sum_iig_i=\\sum_iih_i<\\infty,$ then \\[D(h|f)\\geq D(h|g)+D(g|f),\\] where $D(\\cdot|\\cdot)$ denotes the Kullback--Leibler divergence. These inequalities, interesting in themselves, are also applied to several problems, including maximum entropy characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2043","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"}