problem with Copula Frank samples

[Santymax98]

Hi, I had a very strange problem, when I want to sample the two-dimensional Frank copula I get infinite values.

F = FrankCopula(2,98.11)
r = rand(F,1)
Just with one value, it is giving infinity

I also tried with parameters like 86.44 and 75.

[Santymax98]

I realized that if you use a parameter greater than or equal to 38 the samples start to come out infinite.

[lrnv]

There are overflow happening, this is a pitty. You may obtain the right answer by use bigfloats :

julia> BF = FrankCopula(2,big(100.0))
FrankCopula{2, BigFloat}(θ=100.0)

julia> rand(BF)
2-element Vector{Float64}:
 0.9345996751765854
 0.9568914260322661

However, it looks like it might be possible to achieve the same kind of results with Float64 by leveraging the LogExpFunctions.logm1exp() function if we take enough care, I tried a few things in #65 without much success for the moment, but I do not give up. You may take a look if you want :)

[lrnv]

Another option (the one chosen by the R package) is to just give up and furnish MCopula samples instead for theta > 38 ( they also have a hardcoded 38 there, you did find the right value). But I am not sure I am willing to do that without at least a warning..

[Santymax98]

I am working with dynamic copulas, that is, the parameter can change over time and in the simulations it gives some parameters a little greater than 30, I think that for now I will use the BigFloat option, it is strange that for very small negative values, for example -120 he gives samples without problems

[lrnv]

Did you took a look at those samples ? They might not be very good ones. In #65 I am actually adding a test on uniformity of marginals to check for these kind of stuff more seriously in the future.