← Mathematical handbook

Remark 10: the deterministic boundary in SI and SD classes

theorem Papers.OrendayLaresRockel2026XiBeta.si_xi_one_iff (C : ProbabilityTheory.Copula 2) (hC : C.IsSI) : C.chatterjeeXi = 1 ↔ C = ProbabilityTheory.Copula.comonotonic 2

theorem Papers.OrendayLaresRockel2026XiBeta.sd_xi_one_iff (C : ProbabilityTheory.Copula 2) (hC : C.IsSD) : C.chatterjeeXi = 1 ↔ C = ProbabilityTheory.Copula.countermonotonic

theorem Papers.OrendayLaresRockel2026XiBeta.si_xi_one_beta (C : ProbabilityTheory.Copula 2) (hC : C.IsSI) (hxi : C.chatterjeeXi = 1) : C.blomqvistBeta = 1

theorem Papers.OrendayLaresRockel2026XiBeta.sd_xi_one_beta (C : ProbabilityTheory.Copula 2) (hC : C.IsSD) (hxi : C.chatterjeeXi = 1) : C.blomqvistBeta = -1