← Mathematical handbook

Survival invariance of orthant, conditional and Schur orders

theorem Verification.lowerOrthantLE_survival_iff (C D : ProbabilityTheory.Copula 2) : C.survivalCopula.LowerOrthantLE D.survivalCopula ↔ C.LowerOrthantLE D

theorem Verification.isSI_survival_iff (C : ProbabilityTheory.Copula 2) : C.survivalCopula.IsSI ↔ C.IsSI

theorem Verification.schurLE_reflect_second_iff (C D : ProbabilityTheory.Copula 2) : (C.reflect {1}).SchurLE (D.reflect {1}) ↔ C.SchurLE D

theorem Verification.schurLE_reflect_first_iff (C D : ProbabilityTheory.Copula 2) : (C.reflect {0}).SchurLE (D.reflect {0}) ↔ C.SchurLE D

theorem Verification.schurLE_survival_iff (C D : ProbabilityTheory.Copula 2) : C.survivalCopula.SchurLE D.survivalCopula ↔ C.SchurLE D