{"paper":{"title":"Lamperti-type laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lancelot F. James","submitted_at":"2007-08-04T09:17:40Z","abstract_excerpt":"This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an $\\alpha$-stable law, for $0<\\alpha<1$, and the other variable has the law defined by polynomially tilting the density of an $\\alpha$-stable random variable by a factor $\\theta>-\\alpha$. When $\\theta=0$, these variables equate with the ratio investigated by Lamperti [Trans. Amer. Math. Soc. 88 (1958) 380--387] which, remarkably, was shown to have a simple density. This variable arises in a variety of areas and gains importance from a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0618","kind":"arxiv","version":4},"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"}