Pair-copula conditionals

Vine algorithms require bivariate conditional distribution functions and their inverses. The public API is:

hfunc1(C, u, v)
hfunc2(C, u, v)
hinv1(C, q, v)
hinv2(C, q, u)

The aliases h₁, h₂, h₁⁻¹, and h₂⁻¹ are also exported.

Mathematical convention

The inverse functions satisfy approximately

For singular copulas the inverse should be interpreted as a generalized inverse.

Matrix helpers

For bivariate data stored row-wise as an n × 2 matrix, hfunc1(C, U) and hfunc2(C, U) return vectors of conditional probabilities.

using VineCopulas

C = FrankCopula(2, 3.0)
U = [0.2 0.7; 0.5 0.5; 0.8 0.3]

hfunc1(C, U)

3-element Vector{Float64}:
 0.09968132667590679
 0.4999999999999999
 0.900318673324093