Gumbel–Hougaard lower-orthant parameter order #
The two-coordinate logarithmic power norm decreases with its exponent, so the exponential CDF increases with the parameter.
theorem
ProbabilityTheory.Copula.lowerOrthantLE_gumbel
{θ η : ℝ}
(hθ : 1 ≤ θ)
(hη : 1 ≤ η)
(hθη : θ ≤ η)
:
(gumbel θ hθ).LowerOrthantLE (gumbel η hη)
Gumbel–Hougaard increases in lower-orthant order with its parameter.