Frank copula partial_derivative incorrectly documented

[rodrigoaragaosantos]

Environment Details

Please indicate the following details about the environment in which you found the bug:

• Copulas version: 0.8.0
• Python version: 3.8.5
• Operating System: Ubuntu 18.04.6 LTS

Error Description

Documentation for partial derivative of Frank Copula is described as partial derivative w.r.t. first entry, but it's implemented w.r.t. second entry.

Documentation reads: partial_derivative(U, V) = F( V | U )
But code implementation suggests partial_derivative(U, V) = F( U | V ) as seen as https://sdv.dev/Copulas/_modules/copulas/bivariate/frank.html#Frank.partial_derivative

Which exactly matches F( U | V ) as seen in:

which is itself
(self._g(U) * self._g(V) + self._g(U)) / (self._g(U) * self._g(V) + self._g(1))

according to the Frank.partial_derivative implementation

Steps to reproduce

[ZZY2537]

Hello, I also found the same problem, how did you modify it? This function exists in both Frank.partial_derivative implementation and bivarior.base.

[rodrigoaragaosantos]

I didn't modify it.
I changed my code to use f(b,a) instead of f(a,b) and rolled with it