copula-package: Multivariate Dependence Modeling with Copulas

copula-packageR Documentation

Multivariate Dependence Modeling with Copulas


The copula package provides (S4) classes of commonly used elliptical, (nested) Archimedean, extreme value and other copula families; methods for density, distribution, random number generation, and plots.

Fitting copula models and goodness-of-fit tests. Independence and serial (univariate and multivariate) independence tests, and other copula related tests.


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The copula package provides

  • Classes (S4) of commonly used copulas including elliptical (normal and t; ellipCopula), Archimedean (Clayton, Gumbel, Frank, Joe, and Ali-Mikhail-Haq; ; archmCopula and acopula), extreme value (Gumbel, Husler-Reiss, Galambos, Tawn, and t-EV; evCopula), and other families (Plackett and Farlie-Gumbel-Morgenstern).

  • Methods for density, distribution, random number generation (dCopula, pCopula and rCopula); bivariate dependence measures (rho, tau, etc), perspective and contour plots.

  • Functions (and methods) for fitting copula models including variance estimates (fitCopula).

  • Independence tests among random variables and vectors.

  • Serial independence tests for univariate and multivariate continuous time series.

  • Goodness-of-fit tests for copulas based on multipliers, and the parametric bootstrap, with several transformation options.

  • Bivariate and multivariate tests of extreme-value dependence.

  • Bivariate tests of exchangeability.

Now with former package nacopula for working with nested Archimedean copulas. Specifically,

  • it provides procedures for computing function values and cube volumes (prob),

  • characteristics such as Kendall's tau and tail dependence coefficients (via family objects, e.g., copGumbel),

  • efficient sampling algorithms (rnacopula),

  • various estimators and goodness-of-fit tests.

  • The package also contains related univariate distributions and special functions such as the Sibuya distribution (Sibuya), the polylogarithm (polylog), Stirling and Eulerian numbers (Eulerian).

Further information is available in the following vignettes:

nacopula-pkg Nested Archimedean Copulas Meet R (../doc/nacopula-pkg.pdf)
Frank-Rmpfr Numerically Stable Frank via Multiprecision in R (../doc/Frank-Rmpfr)

For a list of exported functions, use help(package = "copula").


Yan, J. (2007) Enjoy the Joy of Copulas: With a Package copula. Journal of Statistical Software 21(4), 1–21.

Kojadinovic, I. and Yan, J. (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software 34(9), 1–20.

Hofert, M. and Mächler, M. (2011), Nested Archimedean Copulas Meet R: The nacopula Package., Journal of Statistical Software 39(9), 1–20.

Nelsen, R. B. (2006) An introduction to Copulas. Springer, New York.

See Also

The following CRAN packages currently use (‘depend on’) copula: CoClust, copulaedas, Depela, HAC, ipptoolbox, vines.


## Some of the more important functions (and their examples) are

example(fitCopula)## fitting Copulas
example(fitMvdc)  ## fitting multivariate distributions via Copulas
example(nacopula) ## nested Archimedean Copulas

## Independence Tests:  These also draw a 'Dependogram':
example(indepTest)       ## Testing for Independence
example(serialIndepTest) ## Testing for Serial Independence

copula documentation built on Feb. 16, 2023, 8:46 p.m.