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Spearman's rho of Fréchet and Mardia copulas

theorem ProbabilityTheory.Copula.spearmanRho_frechet (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b ≤ 1) : (frechet a b ha hb hab).spearmanRho = a - b

theorem ProbabilityTheory.Copula.spearmanRho_mardia (θ : ℝ) (hθ : |θ| ≤ 1) : (mardia θ hθ).spearmanRho = θ ^ 3