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rcopula

Copula modelling in Python, replicating R's copula package and verified against it — every deterministic quantity is checked against fixtures generated by running the real R package.

pip install rcopula            # core library
pip install "rcopula[plots]"   # plus matplotlib, for rcopula.plots

import rcopula as rc

cop = rc.ClaytonCopula(theta=2.0, dim=3)
u = cop.rvs(1000, random_state=42)

cop.pdf(u), cop.cdf(u)
cop.tau(), cop.rho(), cop.lambda_()

res = rc.fit(rc.GumbelCopula(), u[:, :2], method="mpl")
print(res.summary())  # estimate, standard error, z, p-value, AIC, BIC

What this has that Python did not

  • Standard errors for a fitted copula. No other Python package returns one.
  • The multiplier-bootstrap goodness-of-fit test, which is orders of magnitude faster than the parametric bootstrap.
  • Nested Archimedean copulas — dependence that varies by branch of a tree. These need an exponentially tilted stable sampler that exists nowhere else in the Python ecosystem.
  • Khoudraji's device, mixtures and rotations, so asymmetry and two-tailed dependence do not require a new family.
  • The Kendall distribution function and Kendall return periods.
  • Automatic family selection: rc.select_copula(u) fits every admissible family and ranks them, reporting the tail dependence next to each score.
  • Families missing elsewhere under one API: Joe, AMH, Plackett, FGM, Marshall–Olkin, Galambos, Hüsler–Reiss, Tawn, t-EV, Fréchet bounds.

The one number to take away

Two copulas fitted to the same data, with the same Kendall's τ, disagree about the things you care about:

At τ = 0.5 Clayton Gumbel
99% expected shortfall, two-line loss portfolio 8.57 10.95
Kendall return period at the 99% critical layer 6689 years 199 years
Operational-risk capital, seven cells baseline +20%

A rank correlation, however carefully estimated, does not determine the answer. Choosing the family is the modelling decision.

Licence

MIT. R's copula is GPL-3 and is used solely as a behavioural test oracle — no R source was read to write this package. See NOTICE and CONTRIBUTING.md.