Exact Nelsen 8 tail dependence #
Both tail coefficients vanish for every finite θ ≥ 1, including the countermonotonic endpoint θ = 1.
theorem
ProbabilityTheory.Copula.hasUpperTailDependence_nelsen8
(θ : ℝ)
(hθ : 1 ≤ θ)
:
(nelsen8 θ hθ).HasUpperTailDependence 0
The Nelsen 8 upper-tail coefficient vanishes for all admissible parameters.
theorem
ProbabilityTheory.Copula.hasLowerTailDependence_nelsen8
(θ : ℝ)
(hθ : 1 ≤ θ)
:
(nelsen8 θ hθ).HasLowerTailDependence 0
The Nelsen 8 lower-tail coefficient vanishes for all admissible parameters.