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Table 3: Frank conditional monotonicity and quadrant dependence

theorem Papers.AnsariRockel2024.frank_positive_ci (θ : ℝ) (hθ : 0 < θ) : (ProbabilityTheory.Copula.frank θ hθ).IsCI

theorem Papers.AnsariRockel2024.frank_positive_not_cd (θ : ℝ) (hθ : 0 < θ) : ¬(ProbabilityTheory.Copula.frank θ hθ).IsCD

theorem Papers.AnsariRockel2024.frank_negative_cd (θ : ℝ) (hθ : θ < 0) : (ProbabilityTheory.Copula.frankNegative θ hθ).IsCD

theorem Papers.AnsariRockel2024.frank_negative_not_ci (θ : ℝ) (hθ : θ < 0) : ¬(ProbabilityTheory.Copula.frankNegative θ hθ).IsCI

theorem Papers.AnsariRockel2024.frank_positive_quadrant (θ : ℝ) (hθ : 0 < θ) : (ProbabilityTheory.Copula.frank θ hθ).IsPQD ∧ ¬(ProbabilityTheory.Copula.frank θ hθ).IsNQD

theorem Papers.AnsariRockel2024.frank_negative_quadrant (θ : ℝ) (hθ : θ < 0) : (ProbabilityTheory.Copula.frankNegative θ hθ).IsNQD ∧ ¬(ProbabilityTheory.Copula.frankNegative θ hθ).IsPQD

theorem Papers.AnsariRockel2024.frank_negative_not_density_tp2 (θ : ℝ) (hθ : θ < 0) : ¬(ProbabilityTheory.Copula.frankNegative θ hθ).HasMTP2Density

theorem Papers.AnsariRockel2024.frank_zero_ci_cd : (ProbabilityTheory.Copula.independence 2).IsCI ∧ (ProbabilityTheory.Copula.independence 2).IsCD