I'm facing a stochastic model which needs the copula tool to formulate the dependence within several random variables. For the unknown dependence structure, it would be better if as more the copula families as possible are supported, such as Archimedean copulas, Elliptic copulas, Extreme Value copulas and Vine copulas. Moreover, some dependence measures like Kendall's tau, Spearman's rho and tail dependence are expected to contain in the Python package. And another fundamental functions like PDF, CDF, conditional PDF are also well implemented. The efficient implemementation of the package is also expected.
I have tried the following packages:
openturnsstatsmodelscopulaspycoppyvinecopulib
and the UQLab in MATLAB, but no one can support all the requirements I listed above. openturns is the almost best answer but it doesn't support the rotated Archimedean copulas and Vine copulas and its conditional PDF is somewhat strange. For pyvinecopulib, it seems that the marginal distributions are not supported. pycop only support the survial copula of Archimedean copulas though it's called the rotated Archimedean copulas. copulas support calculating copula's parameter $\theta$ by Kendall's $\tau$ but it doesn't contain complex copula. UQLab doesn't have PDF function.