{"paper":{"title":"On Kendall's Tau for Order Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Klaus D. Schmidt, Sebastian Fuchs","submitted_at":"2018-08-03T11:14:10Z","abstract_excerpt":"Every copula $ C $ for a random vector $ {\\bf X}=(X_1,\\dots,X_d) $ with identically distributed coordinates determines a unique copula $ C_{:d} $ for its order statistic $ {\\bf X}_{:d}=(X_{1:d},\\dots,X_{d:d}) $. In the present paper we study the dependence structure of $ C_{:d} $ via Kendall's tau, denoted by $ \\kappa $. As a general result, we show that $ \\kappa[C_{:d}] $ is at least as large as $ \\kappa[C] $. For the product copula $ \\Pi $, which corresponds to the case of independent coordinates of $ {\\bf X} $, we provide an explicit formula for $ \\kappa[\\Pi_{:d}] $ showing that the inequal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01156","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"}