# copula-package: Multivariate Dependence Modeling with Copulas In copula: Multivariate Dependence with Copulas

 copula-package R Documentation

## Multivariate Dependence Modeling with Copulas

### Description

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.

### Details

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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")`.

### References

Yan, J. (2007) Enjoy the Joy of Copulas: With a Package copula. Journal of Statistical Software 21(4), 1–21. https://www.jstatsoft.org/v21/i04/.

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. https://www.jstatsoft.org/v34/i09/.

Hofert, M. and Mächler, M. (2011), Nested Archimedean Copulas Meet R: The nacopula Package., Journal of Statistical Software 39(9), 1–20. https://www.jstatsoft.org/v39/i09/.

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

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

### Examples

```## 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.