{"paper":{"title":"Existence and non-existence of the non-central Wishart distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\'erard Letac, H\\'el\\`ene Massam","submitted_at":"2011-08-14T07:54:58Z","abstract_excerpt":"The problem considered in this paper is to find when the non-central Wishart distribution, defined on the cone $\\bar{\\mathcal{P}_d}$ of semi positive definite matrices of order $d$ and with a real valued shape parameter, exists. We reduce this problem to the problem of existence of the measures $m(n,k,d)$ defined on $\\bar{\\mathcal{P}_d}$ and with Laplace transform $(\\det s)^{-n/2}\\exp \\tr(s^{-1}w)$ where $n$ is an integer and where $w=\\mathrm{diag}(0,...,0,1,...,1)$ has order $d$ and rank $k.$ We compute $m(d-1,d,d)$ and we show that neither $m(d-2,d,d)$ nor $m(d-2,d-1,d)$ exist. This proves a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2849","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"}