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Papers.AnsariRockel2024.Association

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theorem Papers.AnsariRockel2024.fgm_rho (θ : ℝ) (hθ : |θ| ≤ 1) :
(ProbabilityTheory.Copula.fgm θ hθ).spearmanRho = θ / 3

arXiv:2310.17307v3, Table 6, FGM, Spearman rho. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.fgm_tau (θ : ℝ) (hθ : |θ| ≤ 1) :
(ProbabilityTheory.Copula.fgm θ hθ).kendallTau = 2 * θ / 9

arXiv:2310.17307v3, Table 6, FGM, Kendall tau. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.fgm_xi (θ : ℝ) (hθ : |θ| ≤ 1) :
(ProbabilityTheory.Copula.fgm θ hθ).chatterjeeXi = θ ^ 2 / 15

arXiv:2310.17307v3, Table 6, FGM, Chatterjee xi. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.frechet_rho (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b ≤ 1) :
(ProbabilityTheory.Copula.frechet a b ha hb hab).spearmanRho = a - b

arXiv:2310.17307v3, Table 6, Frechet, Spearman rho. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.frechet_tau (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b ≤ 1) :
(ProbabilityTheory.Copula.frechet a b ha hb hab).kendallTau = (a - b) * (a + b + 2) / 3

arXiv:2310.17307v3, Table 6, Frechet, Kendall tau. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.frechet_xi (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b ≤ 1) :
(ProbabilityTheory.Copula.frechet a b ha hb hab).chatterjeeXi = (a - b) ^ 2 + a * b

arXiv:2310.17307v3, Table 6, Frechet, Chatterjee xi. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.mardia_rho (θ : ℝ) (hθ : |θ| ≤ 1) :
(ProbabilityTheory.Copula.mardia θ hθ).spearmanRho = θ ^ 3

arXiv:2310.17307v3, Table 6, Mardia, Spearman rho. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.mardia_tau (θ : ℝ) (hθ : |θ| ≤ 1) :
(ProbabilityTheory.Copula.mardia θ hθ).kendallTau = θ ^ 3 * (θ ^ 2 + 2) / 3

arXiv:2310.17307v3, Table 6, Mardia, Kendall tau. See COVERAGE.md for conventions.

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theorem Papers.AnsariRockel2024.mardia_xi (θ : ℝ) (hθ : |θ| ≤ 1) :
(ProbabilityTheory.Copula.mardia θ hθ).chatterjeeXi = θ ^ 4 * (1 + 3 * θ ^ 2) / 4

arXiv:2310.17307v3, Table 6, Mardia, Chatterjee xi. See COVERAGE.md for conventions.