{"paper":{"title":"On classical and free stable laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","stat.TH"],"primary_cat":"math.ST","authors_text":"Nizar Demni (PMA)","submitted_at":"2010-09-24T19:56:16Z","abstract_excerpt":"We derive the representative Bernstein measure of the density of $(X_{\\alpha})^{-\\alpha/(1-\\alpha)}, 0 < \\alpha < 1$, where $X_{\\alpha}$ is a positive stable random variable, as a Fox-H function. When $1-\\alpha = 1/j$ for some integer $j \\geq 2$, the Fox H-function reduces to a Meijer G-function so that the Kanter's random variable (see below) is closely related to a product of $(j-1)$ independent Beta random variables. When $\\alpha$ tends to 0, the Bernstein measure becomes degenerate thereby agrees with Cressie's result for the asymptotic behaviour of stable distributions for small values of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4926","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"}