{"paper":{"title":"On the unimodality of power transformations of positive stable densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Thomas Simon (LPP)","submitted_at":"2010-02-19T19:24:31Z","abstract_excerpt":"Let $Z_\\alpha$ be a positive $\\alpha-$stable random variable and $r\\in{\\bf R}.$ We show the existence of an unbounded open domain $D$ in $[1/2,1]\\times{\\bf R}$ with a cusp at $(1/2,-1/2)$, characterized by the complete monotonicity of the function $F_{\\alpha, r} (\\lambda) = (\\alpha \\lambda^\\alpha -r)e^{-\\lambda^\\alpha}/!/! ,$ such that $Z_\\alpha^r$ is unimodal if and only if $(\\alpha, r)\\notin D.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3813","kind":"arxiv","version":3},"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"}