{"paper":{"title":"Tail Behaviour of Weighted Sums of Order Statistics of Dependent Risks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Jinzhi Li","submitted_at":"2014-08-06T14:40:23Z","abstract_excerpt":"Let $X_{1},\\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\\leq \\cdots \\leq X_{n:n}$ of $X_{1},\\ldots ,X_{n}$ under the general case in which the distribution function of $X_{n:n}$ is long-tailed or rapidly varying and $% X_{1},\\ldots ,X_{n}$ may not be comparable in terms of their tail probability. We also present two examples and an application of our results in risk theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1296","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"}