Elliptical CDF

[lrnv]

Gaussian and student have no cdf.

from discourse : https://discourse.julialang.org/t/cdf-of-a-copula-from-copulas-jl/85786

I fixed Copulas.jl (in the latest master commit), so that it provides a more accurate error: we rely on Distributions.jl's implementation of the multivariate Gaussian and Student distributions to handle the complexity behind the Gaussian and Student copulas, and Distributions.jl has no multivariate Gaussian cdf.
Here is a Github issue for this : JuliaStats/Distributions.jl#260
Also, seems relevant there : JuliaStats/StatsFuns.jl#114
But it does not look like it is going to be fixed soon. If you find somewhere an integration routine that computes the cdf of a multivariate Gaussian, I am willing to include it as a temporary workaround though, until those issues are fixed in StatsFun.jl and Distributions.jl

[PharmCat]

Hi!

I think, it can be a concept for GaussianCopula:

using MvNormalCDF
using Copulas, Distributions

x = Normal(0, 1)
y = Normal(0, 2)
C = GaussianCopula([1 0.5; 0.5 1])
D = SklarDist(C, (x,y))

####
μ = mean.(D.m)
σ = collect(std.(D.m))
Σ = cor2cov(D.C.Σ, σ)
MvNormalCDF.mvnormcdf(μ, Σ, [-1.0, -2.0], [3.0, 4.0], m = 6000)
#(0.7216874201273508, 4.10731083253638e-5)
####
func(x) = pdf(D, [x[1], x[2]])
Cubature.pcubature(func, [-1.0, -2.0], [3.0, 4.0], reltol=sqrt(eps()))
#(0.7217122929674319, 8.450906641144229e-12)

cdf could look like this:

function Distributions.cdf(S::SklarDist{<:GaussianCopula, TplMargins}, l, u; kwargs...) where TplMargins
    μ = collect(mean.(S.m))
    σ = collect(std.(D.m))
    Σ = cor2cov(S.C.Σ, σ)
    MvNormalCDF.mvnormcdf(μ, Σ, l, u; kwargs...)
end

[lrnv]

The cdf function already exists for SklarDist and depends on the cdf function of the Copula object. Therefore only the cdf functon of the copula object seems to be needed. I'll try with MvNormalCDF for the gaussian one for now, wait until my PR.