Frank fix + coherence tests on Archimedeans + marginals tests on all copulas

[lrnv]

trying to fix #64, not working yet.

closes #68 too

Relevant sources:

https://github.com/cran/copula/blob/master/src/rLog.c
https://github.com/cran/copula/blob/master/R/frankCopula.R
https://juliastats.org/LogExpFunctions.jl/stable/

[lrnv]

@Santymax98 Look at the new tests, everything is working correclty even for FrankCopula(4,150), without the nasty approximation done in the R package. I also catched a few bugs in other copulas too. Once the tests pass we can merge this.

[Santymax98]

@lrnv
That's great, I'm working a lot with the package, do you think that with those values, the density can be calculated? There are times that, in values for example F = FrankCopula(2.60)
and evaluate it in some style points, den = pdf(F,[0.70, 0.66]) gives an error like
DomainError with 1.0 t - 0.5 t² + 𝒪(t³): The 0-th order coefficient must be non-zero in order to expand `log` around 0.

Does that have to do with the amount of memory required?

[lrnv]

@Santymax98 Could you provide a simple piece of code that shows this error ? I could add it as a test here as i think this PR should solve it, but I am not sure.

Edit: I just added the test and it passes here. Do you have other interesting cases that we could test ? I guess that something more systematic could be done to check pdfs of all copulas at once, the random adding of tests that i am doing here is a bit messy

[codecov]

Codecov Report

Attention: 5 lines in your changes are missing coverage. Please review.

Comparison is base (7b66c5f) 73.81% compared to head (fb27601) 75.87%.
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/univariate_distributions/Logarithmic.jl	87.87%	4 Missing ⚠️
src/ArchimedeanCopulas/FrankCopula.jl	83.33%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #65      +/-   ##
==========================================
+ Coverage   73.81%   75.87%   +2.05%     
==========================================
  Files          28       28              
  Lines         550      572      +22     
==========================================
+ Hits          406      434      +28     
+ Misses        144      138       -6     

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[Santymax98]

I am very bad at writing code in this environment, I think it would be more useful for me to send it by email

[lrnv]

Yes no problem send it by mail or just copy/paste it here :) Know tha tyou can use triple-ticks blocs to format code here:

this is some julia(code)

try to edit this mesage to see the ticks

[lrnv]

I think I will merge this like that and then come back on another PR to fix the issue of the tests not passing on 1.6.