{"paper":{"title":"Log-convexity and log-concavity of noncentral gamma sums and differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Fr\\'ed\\'eric Ouimet, Robert E. Gaunt","submitted_at":"2026-07-10T15:15:36Z","abstract_excerpt":"We study log-convexity and log-concavity of densities obtained from sums and differences of two independent noncentral gamma random variables. We give a complete classification of one-sided log-convexity for noncentral gamma differences, a complete log-convexity classification for sums of two independent central gamma random variables, and sharp log-concavity criteria for central differences and for common-scale sums. As special cases, we deduce a log-convexity classification for the density of the product of two correlated normal random variables with arbitrary means and variances, and log-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09499","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09499/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}