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Genest–Ghoudi dependence properties from Table 3

theorem Papers.AnsariRockel2024.genestGhoudi_not_pqd (θ : ℝ) (hθ : 1 ≤ θ) : ¬(ProbabilityTheory.Copula.genestGhoudi θ hθ).IsPQD

The actual family never has positive quadrant dependence.

theorem Papers.AnsariRockel2024.genestGhoudi_not_ci (θ : ℝ) (hθ : 1 ≤ θ) : ¬(ProbabilityTheory.Copula.genestGhoudi θ hθ).IsCI

No finite family member is conditionally increasing.

theorem Papers.AnsariRockel2024.genestGhoudi_cd_iff (θ : ℝ) (hθ : 1 ≤ θ) : (ProbabilityTheory.Copula.genestGhoudi θ hθ).IsCD ↔ θ = 1

CD holds exactly at the countermonotonic endpoint.

theorem Papers.AnsariRockel2024.genestGhoudi_not_tp2_cdf (θ : ℝ) (hθ : 1 ≤ θ) : ¬(ProbabilityTheory.Copula.genestGhoudi θ hθ).IsTP2CDF

The actual CDF is not TP2 at any finite admissible parameter.

theorem Papers.AnsariRockel2024.genestGhoudi_not_mtp2_density (θ : ℝ) (hθ : 1 ≤ θ) : ¬(ProbabilityTheory.Copula.genestGhoudi θ hθ).HasMTP2Density

The actual copula admits no MTP2 Lebesgue density.