Multivariate Dependence with Copulas

Classes (S4) of commonly used elliptical, Archimedean, extreme-value and other copula families, as well as their rotations, mixtures and asymmetrizations. Nested Archimedean copulas, related tools and special functions. Methods for density, distribution, random number generation, bivariate dependence measures, Rosenblatt transform, Kendall distribution function, perspective and contour plots. Fitting of copula models with potentially partly fixed parameters, including standard errors. Serial independence tests, copula specification tests (independence, exchangeability, radial symmetry, extreme-value dependence, goodness-of-fit) and model selection based on cross-validation. Empirical copula, smoothed versions, and non-parametric estimators of the Pickands dependence function.


Reference manual

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1.0-1 by Martin Maechler, a year ago

Browse source code at

Authors: Marius Hofert [aut] , Ivan Kojadinovic [aut] , Martin Maechler [aut, cre] , Jun Yan [aut] , Johanna G. NeŇ°lehov√° [ctb] (evTestK() , , Rebecca Morger [ctb] ( code for free mixCopula weight parameters)

Documentation:   PDF Manual  

Task views: Probability Distributions, Empirical Finance, Multivariate Statistics, Extreme Value Analysis

GPL (>= 3) | file LICENCE license

Imports stats, graphics, methods, stats4, Matrix, lattice, colorspace, gsl, ADGofTest, stabledist, mvtnorm, pcaPP, pspline, numDeriv

Suggests MASS, KernSmooth, sfsmisc, scatterplot3d, Rmpfr, bbmle, knitr, rmarkdown, abind, crop, gridExtra, lcopula, mev, mvnormtest, parallel, partitions, polynom, qrng, randtoolbox, rugarch, Runuran, tseries, VGAM, VineCopula, zoo

Enhances nor1mix, copulaData

System requirements: pdfcrop (part of TexLive) is required to rebuild the vignettes.

Imported by BSL, ClustImpute, CompAREdesign, CopulaCenR, EFDR, ExtremalDep, ExtremeRisks, GJRM, Omisc, PAsso, PortRisk, bivgeom, bivquant, cascsim, cds, copulaedas, cylcop, depcoeff, drought, flood, gamCopula, gnn, good, mobirep, multinma, mvnormalTest, nvmix, pgee.mixed, qad, qrng, sgee, surrosurv, survivalMPLdc, svars, tailDepFun, zipfextR.

Depended on by BivarP, COST, ClusterStability, CoClust, CoImp, CopCTS, HAC, HMMcopula, NCSCopula, RGENERATEPREC, VC2copula, censorcopula, gofCopula, ipptoolbox, lcopula, nCopula, vfcp, vines.

Suggested by SimDesign, copBasic, docopulae, intcensROC, kyotil, npcp, qrmtools, robustrank, simsalapar, simsem, univariateML, wdm, zenplots.

See at CRAN