{"paper":{"title":"Conditional Limit Results for Type I Polar Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Enkelejd Hashorva","submitted_at":"2008-10-08T22:16:55Z","abstract_excerpt":"Let (S_1,S_2)=(R \\cos(\\Theta), R \\sin (\\Theta)) be a bivariate random vector with associated random radius R which has distribution function $F$ being further independent of the random angle \\Theta. In this paper we investigate the asymptotic behaviour of the conditional survivor probability \\Psi_{\\rho,u}(y):=\\pk{\\rho S_1+ \\sqrt{1- \\rho^2} S_2> y \\lvert S_1> u}, \\rho \\in (-1,1),\\in R when u approaches the upper endpoint of F. On the density function of \\Theta we require a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1547","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"}