Table 5: Tawn conditional increase and both directional Schur orders #
theorem
Papers.AnsariRockel2024.tawn_ci
(θ : ℝ)
(hθ : 1 ≤ θ)
(α β : ↑unitInterval)
:
(ProbabilityTheory.Copula.tawn θ hθ α β).IsCI
theorem
Papers.AnsariRockel2024.tawn_schur_monotone
{θ η : ℝ}
(hθ : 1 ≤ θ)
(hθη : θ ≤ η)
(α β : ↑unitInterval)
:
(ProbabilityTheory.Copula.tawn θ hθ α β).SchurBothLE (ProbabilityTheory.Copula.tawn η ⋯ α β)
theorem
Papers.AnsariRockel2024.maxProduct_independence_ci
(C : ProbabilityTheory.Copula 2)
(hC : C.IsCI)
(α β : ↑unitInterval)
:
(C.maxProduct (ProbabilityTheory.Copula.independence 2) ![α, β]).IsCI
The closure argument used for the asymmetric logistic family includes all weight endpoints.