← Copula mathematical handbook

Reflection of the response coordinate preserves directional xi

theorem ProbabilityTheory.Copula.RankRegion.Common.conditionalCDF_reflect_second (C : Copula 2) (v : ↑unitInterval) : (fun (u : ↑unitInterval) => (C.reflect {1}).conditionalCDF u v) =ᵐ[MeasureTheory.volume] fun (u : ↑unitInterval) => 1 - C.conditionalCDF u (unitInterval.symm v)

theorem ProbabilityTheory.Copula.RankRegion.Common.xi_reflect_second (C : Copula 2) : (C.reflect {1}).chatterjeeXi = C.chatterjeeXi