Exact Joe tail dependence #
Both limits hold for every finite θ ≥ 1, including the independence endpoint.
theorem
ProbabilityTheory.Copula.hasLowerTailDependence_joe
(θ : ℝ)
(hθ : 1 ≤ θ)
:
(joe θ hθ).HasLowerTailDependence 0
theorem
ProbabilityTheory.Copula.hasUpperTailDependence_joe
(θ : ℝ)
(hθ : 1 ≤ θ)
:
(joe θ hθ).HasUpperTailDependence (2 - 2 ^ θ⁻¹)
Joe's upper-tail coefficient for every parameter, including θ = 1.