copula-package {copula} | 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
The DESCRIPTION file:
Package: | copula |
Version: | 1.1-3 |
VersionNote: | Last CRAN: 1.1-2 on 2023-01-20 |
Date: | 2023-12-07 |
Title: | Multivariate Dependence with Copulas |
Authors@R: | c(person("Marius", "Hofert", role = "aut", email = "marius.hofert@uwaterloo.ca", comment = c(ORCID = "0000-0001-8009-4665")) , person("Ivan", "Kojadinovic", role = "aut", email = "ivan.kojadinovic@univ-pau.fr", comment = c(ORCID = "0000-0002-2903-1543")) , person("Martin","Maechler", role=c("aut","cre"), email="maechler@stat.math.ethz.ch", comment = c(ORCID = "0000-0002-8685-9910")) , person("Jun", "Yan", role = "aut", email = "jun.yan@uconn.edu", comment = c(ORCID = "0000-0003-4401-7296")) , person(c("Johanna", "G."), "Nešlehová", role = "ctb", comment = c("evTestK()", ORCID = "0000-0001-9634-4796")) , person("Rebecca", "Morger", role = "ctb", comment = "fitCopula.ml(): code for free mixCopula weight parameters") ) |
Depends: | R (>= 3.5.0) |
Imports: | stats, graphics, methods, stats4, Matrix (>= 1.5-0), lattice, colorspace, gsl, ADGofTest, stabledist (>= 0.6-4), 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 |
SuggestsNote: | packages {abind, ..., zoo} (last lines above) are only used in vignettes, demos and a few tests. |
VignetteBuilder: | knitr |
Enhances: | nor1mix, copulaData |
SystemRequirements: | pdfcrop (part of TexLive) is required to rebuild the vignettes. |
Description: | 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. |
License: | GPL (>= 3) | file LICENCE |
Collate: | AllClass.R Classes.R AllGeneric.R Auxiliaries.R aux-acopula.R asymCopula.R mixCopula.R rotCopula.R Copula.R special-func.R amhCopula.R claytonCopula.R frankCopula.R cop_objects.R nacopula.R dC-dc.R amhExpr.R An.R archmCopula.R cCopula.R claytonExpr.R ellipCopula.R empCopula.R empPsi.R acR.R estimation.R evCopula.R evTests.R exchTests.R fgmCopula.R fitCopula.R fitLambda.R fitMvdc.R fixedPar.R frankExpr.R galambosCopula.R galambosExpr-math.R galambosExpr.R ggraph-tools.R pairsRosenblatt.R prob.R gofTrafos.R gofEVTests.R gofCopula.R graphics.R gumbelCopula.R gumbelExpr.R huslerReissCopula.R huslerReissExpr.R indepCopula.R fhCopula.R lowfhCopula.R upfhCopula.R indepTests.R joeCopula.R K.R logseries.R mvdc.R margCopula.R matrix_tools.R normalCopula.R obs.R opower.R plackettCopula.R plackettExpr.R moCopula.R rstable1.R safeUroot.R schlatherCopula.R stable.R timing.R tCopula.R tawnCopula.R tawnExpr.R tevCopula.R varianceReduction.R wrapper.R xvCopula.R zzz.R |
Encoding: | UTF-8 |
URL: | https://copula.r-forge.r-project.org/, https://r-forge.r-project.org/projects/copula/, https://CRAN.r-project.org/package=copula |
BugReports: | https://r-forge.r-project.org/tracker/?func=add&group_id=2140&atid=5417 |
Author: | Marius Hofert [aut] (<https://orcid.org/0000-0001-8009-4665>), Ivan Kojadinovic [aut] (<https://orcid.org/0000-0002-2903-1543>), Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Jun Yan [aut] (<https://orcid.org/0000-0003-4401-7296>), Johanna G. Nešlehová [ctb] (evTestK(), <https://orcid.org/0000-0001-9634-4796>), Rebecca Morger [ctb] (fitCopula.ml(): code for free mixCopula weight parameters) |
Maintainer: | Martin Maechler <maechler@stat.math.ethz.ch> |
Index of help topics:
.pairsCond Pairs Plot of a cu.u Object (Internal Use) A..Z Sinc, Zolotarev's, and Other Mathematical Utility Functions An Nonparametric Rank-based Estimators of the Pickands Dependence Function Bernoulli Compute Bernoulli Numbers Copula Density, Evaluation, and Random Number Generation for Copula Functions Eulerian Eulerian and Stirling Numbers of First and Second Kind K Kendall Distribution Function for Archimedean Copulas Mvdc Multivariate Distributions Constructed from Copulas RSpobs Pseudo-Observations of Radial and Uniform Part of Elliptical and Archimedean Copulas SMI.12 SMI Data - 141 Days in Winter 2011/2012 Sibuya Sibuya Distribution - Sampling and Probabilities absdPsiMC Absolute Value of Generator Derivatives via Monte Carlo acopula-class Class "acopula" of Archimedean Copula Families acopula-families Specific Archimedean Copula Families ("acopula" Objects) allComp All Components of a (Inner or Outer) Nested Archimedean Copula archmCopula Construction of Archimedean Copula Class Object archmCopula-class Class "archmCopula" beta. Sample and Population Version of Blomqvist's Beta for Archimedean Copulas cCopula Conditional Distributions and Their Inverses from Copulas cloud2-methods Cloud Plot Methods ('cloud2') in Package 'copula' coeffG Coefficients of Polynomial used for Gumbel Copula contour-methods Methods for Contour Plots in Package 'copula' contourplot2-methods Contour Plot Methods 'contourplot2' in Package 'copula' copula-class Mother Classes "Copula", etc of all Copulas in the Package copula-package Multivariate Dependence Modeling with Copulas corKendall (Fast) Computation of Pairwise Kendall's Taus dDiag Density of the Diagonal of (Nested) Archimedean Copulas describeCop Copula (Short) Description as String dnacopula Density Evaluation for (Nested) Archimedean Copulas ebeta Various Estimators for (Nested) Archimedean Copulas ellipCopula Construction of Elliptical Copula Class Objects ellipCopula-class Class "ellipCopula" of Elliptical Copulas emde Minimum Distance Estimators for (Nested) Archimedean Copulas emle Maximum Likelihood Estimators for (Nested) Archimedean Copulas empCopula The Empirical Copula empCopula-class Class "empCopula" of Empirical Copulas enacopula Estimation Procedures for (Nested) Archimedean Copulas evCopula Construction of Extreme-Value Copula Objects evCopula-class Classes Representing Extreme-Value Copulas evTestA Bivariate Test of Extreme-Value Dependence Based on Pickands' Dependence Function evTestC Large-sample Test of Multivariate Extreme-Value Dependence evTestK Bivariate Test of Extreme-Value Dependence Based on Kendall's Distribution exchEVTest Test of Exchangeability for Certain Bivariate Copulas exchTest Test of Exchangeability for a Bivariate Copula fgmCopula Construction of a fgmCopula Class Object fgmCopula-class Class "fgmCopula" - Multivariate Multiparameter Farlie-Gumbel-Morgenstern Copulas fhCopula Construction of Fréchet-Hoeffding Bound Copula Objects fhCopula-class Class "fhCopula" of Fréchet-Hoeffding Bound Copulas fitCopula Fitting Copulas to Data - Copula Parameter Estimation fitCopula-class Classes of Fitted Multivariate Models: Copula, Mvdc fitLambda Non-parametric Estimators of the Matrix of Tail-Dependence Coefficients fitMvdc Estimation of Multivariate Models Defined via Copulas fixParam Fix a Subset of a Copula Parameter Vector gasoil Daily Crude Oil and Natural Gas Prices from 2003 to 2006 getAcop Get "acopula" Family Object by Name getIniParam Get Initial Parameter Estimate for Copula getTheta Get the Parameter(s) of a Copula gnacopula Goodness-of-fit Testing for (Nested) Archimedean Copulas gofBTstat Various Goodness-of-fit Test Statistics gofCopula Goodness-of-fit Tests for Copulas gofEVCopula Goodness-of-fit Tests for Bivariate Extreme-Value Copulas gofTstat Goodness-of-fit Test Statistics htrafo GOF Testing Transformation of Hering and Hofert iPsi Generator Functions for Archimedean and Extreme-Value Copulas indepCopula Construction of Independence Copula Objects indepCopula-class Class "indepCopula" indepTest Test Independence of Continuous Random Variables via Empirical Copula initOpt Initial Interval or Value for Parameter Estimation of Archimedean Copulas interval Construct Simple "interval" Object interval-class Class "interval" of Simple Intervals khoudrajiCopula Construction of copulas using Khoudraji's device khoudrajiCopula-class Class '"khoudrajiCopula"' and its Subclasses log1mexp Compute f(a) = log(1 +/- exp(-a)) Numerically Optimally loss LOSS and ALAE Insurance Data margCopula Marginal copula of a Copula With Specified Margins mixCopula Create Mixture of Copulas mixCopula-class Class '"mixCopula"' of Copula Mixtures moCopula The Marshall-Olkin Copula moCopula-class Class "moCopula" of Marshall-Olkin Copulas multIndepTest Independence Test Among Continuous Random Vectors Based on the Empirical Copula Process multSerialIndepTest Serial Independence Test for Multivariate Time Series via Empirical Copula mvdc-class Class "mvdc": Multivariate Distributions from Copulas nacFrail.time Timing for Sampling Frailties of Nested Archimedean Copulas nacPairthetas Pairwise Thetas of Nested Archimedean Copulas nacopula-class Class "nacopula" of Nested Archimedean Copulas nesdepth Nesting Depth of a Nested Archimedean Copula ("nacopula") onacopula Constructing (Outer) Nested Archimedean Copulas opower Outer Power Transformation of Archimedean Copulas p2P Tools to Work with Matrices pacR Distribution of the Radial Part of an Archimedean Copula pairs2 Scatter-Plot Matrix ('pairs') for Copula Distributions with Nice Defaults pairsRosenblatt Plots for Graphical GOF Test via Pairwise Rosenblatt Transforms pairwiseCcop Computations for Graphical GOF Test via Pairwise Rosenblatt Transforms persp-methods Methods for Function 'persp' in Package 'copula' plackettCopula Construction of a Plackett Copula plackettCopula-class Class "plackettCopula" of Plackett Copulas plot-methods Methods for 'plot' in Package 'copula' pnacopula Evaluation of (Nested) Archimedean Copulas pobs Pseudo-Observations polylog Polylogarithm Li_s(z) and Debye Functions polynEval Evaluate Polynomials printNacopula Print Compact Overview of a Nested Archimedean Copula ("nacopula") prob Computing Probabilities of Hypercubes qqplot2 Q-Q Plot with Rugs and Pointwise Asymptotic Confidence Intervals rAntitheticVariates Variance-Reduction Methods rF01Frank Sample Univariate Distributions Involved in Nested Frank and Joe Copulas rFFrank Sampling Distribution F for Frank and Joe radSymTest Test of Exchangeability for a Bivariate Copula rdj Daily Returns of Three Stocks in the Dow Jones retstable Sampling Exponentially Tilted Stable Distributions rlog Sampling Logarithmic Distributions rnacModel Random nacopula Model rnacopula Sampling Nested Archimedean Copulas rnchild Sampling Child 'nacopula's rotCopula Construction and Class of Rotated aka Reflected Copulas rstable1 Random numbers from (Skew) Stable Distributions safeUroot One-dimensional Root (Zero) Finding - Extra "Safety" for Convenience serialIndepTest Serial Independence Test for Continuous Time Series Via Empirical Copula setTheta Specify the Parameter(s) of a Copula show-methods Methods for 'show()' in Package 'copula' splom2-methods Methods for Scatter Plot Matrix 'splom2' in Package 'copula' tau Dependence Measures for Bivariate Copulas tauAMH Ali-Mikhail-Haq ("AMH")'s and Joe's Kendall's Tau uranium Uranium Exploration Dataset of Cook & Johnson (1986) wireframe2-methods Perspective Plots - 'wireframe2' in Package 'copula' xvCopula Model (copula) selection based on 'k'-fold cross-validation
Further information is available in the following vignettes:
AC_Liouville | Archimedean Liouville Copulas (source) |
AR_Clayton | MLE and Quantile Evaluation for a Clayton AR(1) Model with Student Marginals (source) |
GIG | Generalized Inverse Gaussian Archimedean Copulas (source) |
HAXC | Hierarchical Archimax Copulas (source) |
NALC | Nested Archimedean Lévy Copulas (source) |
copula_GARCH | The Copula GARCH Model (source) |
dNAC | Densities of Two-Level Nested Archimedean Copulas (source) |
empiricial_copulas | Exploring Empirical Copulas (source) |
logL_visualization | Log-Likelihood Visualization for Archimedean Copulas (source) |
qrng | Quasi-Random Numbers for Copula Models (source) |
wild_animals | Wild Animals: Examples of Nonstandard Copulas (source) |
Frank-Rmpfr | Numerically stable Frank Copulas via Multiprecision (Rmpfr) (source) |
nacopula-pkg | Nested Archimedean Copulas Meet R (source) |
rhoAMH-dilog | Beautiful Spearman's Rho for AMH Copula (source) |
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
andacopula
), 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
andrCopula
); 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.
See Also
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