| 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; ;archmCopulaandacopula), 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,pCopulaandrCopula); 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
[Package copula version 1.1-3 Index]