Extreme-value pair-copulas

Bivariate extreme-value copulas are supported through the Pickands dependence function representation supplied by Copulas.jl.

For an extreme-value copula,

where is the Pickands dependence function.

Conditional functions

For smooth tails, the implementation uses analytic h-functions derived from and . Inverse conditionals are solved in a safeguarded one-dimensional coordinate. Tails with jumps or flat conditional regions use generalized conditional quantiles.

Tested examples

using VineCopulas
using Copulas

C = Copulas.ExtremeValueCopula(2, Copulas.GalambosTail(1.5))
q = hfunc1(C, 0.3, 0.7)
hinv1(C, q, 0.7)

0.30000000000000016

Tested tails include logistic, Galambos, Hüsler–Reiss, Mixed, asymmetric logistic, asymmetric Galambos, asymmetric Mixed, Cuadras–Augé, Marshall–Olkin, BC2, and extreme-t.

This is one of the distinctive parts of VineCopulas.jl: smooth and singular extreme-value pair-copulas are handled separately instead of pretending that every inverse is an ordinary smooth inverse.