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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.