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Affine dependence coefficients under convex mixtures

Rho, footrule, gamma and beta are affine in the copula. This statement does not extend to Kendall's tau or Chatterjee's xi.

theorem ProbabilityTheory.Copula.spearmanRho_mix (C D : Copula 2) (a : ↑unitInterval) : (C.mix D a).spearmanRho = ↑a * C.spearmanRho + (1 - ↑a) * D.spearmanRho

theorem ProbabilityTheory.Copula.spearmanFootrule_mix (C D : Copula 2) (a : ↑unitInterval) : (C.mix D a).spearmanFootrule = ↑a * C.spearmanFootrule + (1 - ↑a) * D.spearmanFootrule

theorem ProbabilityTheory.Copula.giniGamma_mix (C D : Copula 2) (a : ↑unitInterval) : (C.mix D a).giniGamma = ↑a * C.giniGamma + (1 - ↑a) * D.giniGamma

theorem ProbabilityTheory.Copula.blomqvistBeta_mix (C D : Copula 2) (a : ↑unitInterval) : (C.mix D a).blomqvistBeta = ↑a * C.blomqvistBeta + (1 - ↑a) * D.blomqvistBeta