{"paper":{"title":"Change of measure technique in characterizations of the Gamma and Kummer distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Agnieszka Piliszek, Jacek Weso{\\l}owski","submitted_at":"2017-02-09T14:13:32Z","abstract_excerpt":"If $X$ and $Y$ are independent random variables with distributions $\\mu$ and $\\nu$ then $U=\\psi(X,Y)$ and $V=\\phi(X,Y)$ are also independent for some $\\psi$ and $\\phi$. Properties of this type are known for many important probability distributions $\\mu$ and $\\nu$. Also related characterization questions have been widely investigated: Let $X$ and $Y$ be independent and let $U$ and $V$ be independent. Are the distributions of $X$ and $Y$ $\\mu$ and $\\nu$, respectively? Recently two new properties and characterizations of this kind involving the Kummer distribution appeared in the literature. For "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02839","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"}