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Papers.AnsariRockel2024.NelsenEndpointDependence

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Table 3 dependence properties at the common Clayton(1) endpoint #

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theorem Papers.AnsariRockel2024.nelsen12_ci_one :
(ProbabilityTheory.Copula.nelsen12 1 ⋯).IsCI
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theorem Papers.AnsariRockel2024.nelsen14_ci_one :
(ProbabilityTheory.Copula.nelsen14 1 ⋯).IsCI
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theorem Papers.AnsariRockel2024.nelsen12_tp2_cdf_one :
(ProbabilityTheory.Copula.nelsen12 1 ⋯).IsTP2CDF
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theorem Papers.AnsariRockel2024.nelsen14_tp2_cdf_one :
(ProbabilityTheory.Copula.nelsen14 1 ⋯).IsTP2CDF
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theorem Papers.AnsariRockel2024.nelsen12_mtp2_density_one :
(ProbabilityTheory.Copula.nelsen12 1 ⋯).HasMTP2Density
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theorem Papers.AnsariRockel2024.nelsen14_mtp2_density_one :
(ProbabilityTheory.Copula.nelsen14 1 ⋯).HasMTP2Density
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theorem Papers.AnsariRockel2024.nelsen12_not_cd_one :
¬(ProbabilityTheory.Copula.nelsen12 1 ⋯).IsCD
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theorem Papers.AnsariRockel2024.nelsen14_not_cd_one :
¬(ProbabilityTheory.Copula.nelsen14 1 ⋯).IsCD
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theorem Papers.AnsariRockel2024.nelsen12_pqd (θ : ℝ) (hθ : 1 ≤ θ) :
(ProbabilityTheory.Copula.nelsen12 θ hθ).IsPQD

Nelsen 12 is PQD throughout its full finite parameter range.

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theorem Papers.AnsariRockel2024.nelsen14_pqd (θ : ℝ) (hθ : 1 ≤ θ) :
(ProbabilityTheory.Copula.nelsen14 θ hθ).IsPQD

Nelsen 14 is PQD throughout its full finite parameter range.

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theorem Papers.AnsariRockel2024.nelsen12_not_cd (θ : ℝ) (hθ : 1 ≤ θ) :
¬(ProbabilityTheory.Copula.nelsen12 θ hθ).IsCD

Nelsen 12 is never conditionally decreasing.

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theorem Papers.AnsariRockel2024.nelsen14_not_cd (θ : ℝ) (hθ : 1 ≤ θ) :
¬(ProbabilityTheory.Copula.nelsen14 θ hθ).IsCD

Nelsen 14 is never conditionally decreasing.