{"paper":{"title":"Analytic and asymptotic properties of multivariate generalized Linnik's probability densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"L.P. Teo, S.C. Lim","submitted_at":"2009-03-30T23:44:54Z","abstract_excerpt":"This paper studies the properties of the probability density function $p_{\\alpha,\\nu, n}(\\mathbf{x})$ of the $n$-variate generalized Linnik distribution whose characteristic function $\\varphi_{\\alpha,\\nu,n}(\\boldsymbol{t})$ is given by \\varphi_{\\alpha,\\nu,n}(\\boldsymbol{t})=\\frac{1} {(1+\\Vert\\boldsymbol{t}\\Vert^{\\alpha})^{\\nu}}, \\alpha\\in (0,2], \\nu>0, \\boldsymbol{t}\\in \\mathbb{R}^n, where $\\Vert\\boldsymbol{t}\\Vert$ is the Euclidean norm of $\\boldsymbol{t}\\in\\mathbb{R}^n$. Integral representations of $p_{\\alpha,\\nu, n}(\\mathbf{x})$ are obtained and used to derive the asymptotic expansions of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5344","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":""},"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"}