# Multivariate Dependence with Copulas

## Documentation for package ‘copula’ version 1.1-6

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Code demos. Use demo() to run them.
- Package NEWS.

## Help Pages

A B C D E F G H I J K L M N O P Q R S T U V W X misc

copula-package | Multivariate Dependence Modeling with Copulas

## -- A --

A | Generator Functions for Archimedean and Extreme-Value Copulas
A-method | Generator Functions for Archimedean and Extreme-Value Copulas
A-methods | Generator Functions for Archimedean and Extreme-Value Copulas
A..Z | Sinc, Zolotarev's, and Other Mathematical Utility Functions
absdPsiMC | Absolute Value of Generator Derivatives via Monte Carlo
acopula | Class "acopula" of Archimedean Copula Families
acopula-class | Class "acopula" of Archimedean Copula Families
acopula-families | Specific Archimedean Copula Families ("acopula" Objects)
Afun | Generator Functions for Archimedean and Extreme-Value Copulas
AfunDer | Generator Functions for Archimedean and Extreme-Value Copulas
allComp | All Components of a (Inner or Outer) Nested Archimedean Copula
amhCopula | Construction of Archimedean Copula Class Object
amhCopula-class | Class "archmCopula"
An | Nonparametric Rank-based Estimators of the Pickands Dependence Function
An.biv | Nonparametric Rank-based Estimators of the Pickands Dependence Function
Anfun | Nonparametric Rank-based Estimators of the Pickands Dependence Function
archmCopula | Construction of Archimedean Copula Class Object
archmCopula-class | Class "archmCopula"
asym2Copula-class | Class '"khoudrajiCopula"' and its Subclasses
asymCopula | Construction of copulas using Khoudraji's device
asymCopula-class | Class '"khoudrajiCopula"' and its Subclasses
asymExplicitCopula | Construction of copulas using Khoudraji's device

## -- B --

Bernoulli | Compute Bernoulli Numbers
Bernoulli.all | Compute Bernoulli Numbers
beta. | Sample and Population Version of Blomqvist's Beta for Archimedean Copulas
beta.hat | Sample and Population Version of Blomqvist's Beta for Archimedean Copulas
betan | Sample and Population Version of Blomqvist's Beta for Archimedean Copulas

## -- C --

C.n | The Empirical Copula
cacopula | Conditional Distributions and Their Inverses from Copulas
calibKendallsTau | Dependence Measures for Bivariate Copulas
calibSpearmansRho | Dependence Measures for Bivariate Copulas
cCopula | Conditional Distributions and Their Inverses from Copulas
claytonCopula | Construction of Archimedean Copula Class Object
claytonCopula-class | Class "archmCopula"
cloud2 | Cloud Plot Methods ('cloud2') in Package 'copula'
cloud2-method | Cloud Plot Methods ('cloud2') in Package 'copula'
cloud2-methods | Cloud Plot Methods ('cloud2') in Package 'copula'
Cn | The Empirical Copula
coef.fittedMV | Estimation of Multivariate Models Defined via Copulas
coeffG | Coefficients of Polynomial used for Gumbel Copula
contour-method | Methods for Contour Plots in Package 'copula'
contour-methods | Methods for Contour Plots in Package 'copula'
contourplot2 | Contour Plot Methods 'contourplot2' in Package 'copula'
contourplot2-method | Contour Plot Methods 'contourplot2' in Package 'copula'
contourplot2-methods | Contour Plot Methods 'contourplot2' in Package 'copula'
copAMH | Specific Archimedean Copula Families ("acopula" Objects)
copClayton | Specific Archimedean Copula Families ("acopula" Objects)
copFrank | Specific Archimedean Copula Families ("acopula" Objects)
copGumbel | Specific Archimedean Copula Families ("acopula" Objects)
copJoe | Specific Archimedean Copula Families ("acopula" Objects)
Copula | Density, Evaluation, and Random Number Generation for Copula Functions
Copula-class | Mother Classes "Copula", etc of all Copulas in the Package
copula-class | Mother Classes "Copula", etc of all Copulas in the Package
corKendall | (Fast) Computation of Pairwise Kendall's Taus

## -- D --

dAdu | Generator Functions for Archimedean and Extreme-Value Copulas
dAdu-method | Generator Functions for Archimedean and Extreme-Value Copulas
dAdu-methods | Generator Functions for Archimedean and Extreme-Value Copulas
dCn | The Empirical Copula
dCopula | Density, Evaluation, and Random Number Generation for Copula Functions
dcopula | Density, Evaluation, and Random Number Generation for Copula Functions
dCopula-method | Density, Evaluation, and Random Number Generation for Copula Functions
dCopula-method | Density Evaluation for (Nested) Archimedean Copulas
dDiag | Density of the Diagonal of (Nested) Archimedean Copulas
debye1 | Polylogarithm Li_s(z) and Debye Functions
debye2 | Polylogarithm Li_s(z) and Debye Functions
dependogram | Test Independence of Continuous Random Variables via Empirical Copula
describeCop | Copula (Short) Description as String
describeCop-method | Copula (Short) Description as String
describeCop-methods | Copula (Short) Description as String
dim-method | Class '"khoudrajiCopula"' and its Subclasses
dim-method | Mother Classes "Copula", etc of all Copulas in the Package
dim-method | Class "empCopula" of Empirical Copulas
dim-method | Class '"mixCopula"' of Copula Mixtures
dim-method | Class "mvdc": Multivariate Distributions from Copulas
dim-method | Class "nacopula" of Nested Archimedean Copulas
dim-method | Construction and Class of Rotated aka Reflected Copulas
dimCopula-class | Mother Classes "Copula", etc of all Copulas in the Package
diPsi | Generator Functions for Archimedean and Extreme-Value Copulas
diPsi-method | Generator Functions for Archimedean and Extreme-Value Copulas
diPsi-methods | Generator Functions for Archimedean and Extreme-Value Copulas
dispstrToep | Construction of Elliptical Copula Class Objects
dK | Kendall Distribution Function for Archimedean Copulas
dMvdc | Multivariate Distributions Constructed from Copulas
dmvdc | Multivariate Distributions Constructed from Copulas
dnacopula | Density Evaluation for (Nested) Archimedean Copulas
dSibuya | Sibuya Distribution - Sampling and Probabilities
dsumSibuya | Sibuya Distribution - Sampling and Probabilities

## -- E --

ebeta | Various Estimators for (Nested) Archimedean Copulas
edmle | 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
etau | Various Estimators for (Nested) Archimedean Copulas
Eulerian | Eulerian and Stirling Numbers of First and Second Kind
Eulerian.all | Eulerian and Stirling Numbers of First and Second Kind
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
extremePairs | Tools to Work with Matrices

## -- F --

F.n | The Empirical 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
fitCopula-method | Fitting Copulas to Data - Copula Parameter Estimation
fitCopula-methods | Fitting Copulas to Data - Copula Parameter Estimation
fitLambda | Non-parametric Estimators of the Matrix of Tail-Dependence Coefficients
fitMvdc | Estimation of Multivariate Models Defined via Copulas
fitMvdc-class | Classes of Fitted Multivariate Models: Copula, Mvdc
fittedMV-class | Classes of Fitted Multivariate Models: Copula, Mvdc
fixedParam<- | Fix a Subset of a Copula Parameter Vector
fixedParam<--method | Fix a Subset of a Copula Parameter Vector
fixParam | Fix a Subset of a Copula Parameter Vector
format-method | Class "interval" of Simple Intervals
frankCopula | Construction of Archimedean Copula Class Object
frankCopula-class | Class "archmCopula"

## -- G --

galambosCopula | Construction of Extreme-Value Copula Objects
galambosCopula-class | Classes Representing Extreme-Value Copulas
gasoil | Daily Crude Oil and Natural Gas Prices from 2003 to 2006
genFun | Generator Functions for Archimedean and Extreme-Value Copulas
genFunDer1 | Generator Functions for Archimedean and Extreme-Value Copulas
genFunDer2 | Generator Functions for Archimedean and Extreme-Value Copulas
genInv | Generator Functions for Archimedean and Extreme-Value Copulas
getAcop | Get "acopula" Family Object by Name
getAname | Get "acopula" Family Object by Name
getIniParam | Get Initial Parameter Estimate for Copula
getIniParam-method | Get Initial Parameter Estimate for Copula
getSigma | Tools to Work with Matrices
getTheta | Get the Parameter(s) of a Copula
getTheta-method | Get the Parameter(s) of a Copula
getTheta-methods | 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
gofCopula-method | Goodness-of-fit Tests for Copulas
gofCopula-methods | Goodness-of-fit Tests for Copulas
gofEVCopula | Goodness-of-fit Tests for Bivariate Extreme-Value Copulas
gofMB | Goodness-of-fit Tests for Copulas
gofPB | Goodness-of-fit Tests for Copulas
gofT2stat | Goodness-of-fit Test Statistics
gofTstat | Goodness-of-fit Test Statistics
gpviTest | Computations for Graphical GOF Test via Pairwise Rosenblatt Transforms
gumbelCopula | Construction of Archimedean Copula Class Object
gumbelCopula-class | Class "archmCopula"

## -- H --

htrafo | GOF Testing Transformation of Hering and Hofert
huslerReissCopula | Construction of Extreme-Value Copula Objects
huslerReissCopula-class | Classes Representing Extreme-Value Copulas

## -- I --

indepCopula | Construction of Independence Copula Objects
indepCopula-class | Class "indepCopula"
indepTest | Test Independence of Continuous Random Variables via Empirical Copula
indepTestSim | Test Independence of Continuous Random Variables via Empirical Copula
initialize-method | Class "acopula" of Archimedean Copula Families
initOpt | Initial Interval or Value for Parameter Estimation of Archimedean Copulas
interval | Construct Simple "interval" Object
interval-class | Class "interval" of Simple Intervals
iPsi | Generator Functions for Archimedean and Extreme-Value Copulas
iPsi-method | Generator Functions for Archimedean and Extreme-Value Copulas
iPsi-methods | Generator Functions for Archimedean and Extreme-Value Copulas
iRho | Dependence Measures for Bivariate Copulas
iRho-method | Dependence Measures for Bivariate Copulas
iRho-methods | Dependence Measures for Bivariate Copulas
isFree | Fix a Subset of a Copula Parameter Vector
isFree-method | Fix a Subset of a Copula Parameter Vector
isFreeP | Fix a Subset of a Copula Parameter Vector
iTau | Dependence Measures for Bivariate Copulas
iTau-method | Dependence Measures for Bivariate Copulas
iTau-methods | Dependence Measures for Bivariate Copulas

## -- J --

joeCopula | Construction of Archimedean Copula Class Object
joeCopula-class | Class "archmCopula"

## -- K --

K | Kendall Distribution Function for Archimedean Copulas
kendallsTau | Dependence Measures for Bivariate Copulas
khoudrajiBivCopula-class | Class '"khoudrajiCopula"' and its Subclasses
khoudrajiCopula | Construction of copulas using Khoudraji's device
khoudrajiCopula-class | Class '"khoudrajiCopula"' and its Subclasses
khoudrajiExplicitCopula-class | Class '"khoudrajiCopula"' and its Subclasses
Kn | Kendall Distribution Function for Archimedean Copulas

## -- L --

lambda | Dependence Measures for Bivariate Copulas
lambda-method | Dependence Measures for Bivariate Copulas
lambda-method | Class '"mixCopula"' of Copula Mixtures
lambda-methods | Dependence Measures for Bivariate Copulas
log1mexp | Compute f(a) = log(1 +/- exp(-a)) Numerically Optimally
log1pexp | Compute f(a) = log(1 +/- exp(-a)) Numerically Optimally
logLik.fittedMV | Estimation of Multivariate Models Defined via Copulas
loglikCopula | Fitting Copulas to Data - Copula Parameter Estimation
loglikCopulaMany | Fitting Copulas to Data - Copula Parameter Estimation
loglikMvdc | Estimation of Multivariate Models Defined via Copulas
loss | LOSS and ALAE Insurance Data
lowfhCopula | Construction of Fréchet-Hoeffding Bound Copula Objects
lowfhCopula-class | Class "fhCopula" of Fréchet-Hoeffding Bound Copulas
lSMI | SMI Data - 141 Days in Winter 2011/2012

## -- M --

margCopula | Marginal copula of a Copula With Specified Margins
margCopula-method | Marginal copula of a Copula With Specified Margins
maybeInterval-class | Class "interval" of Simple Intervals
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 | Multivariate Distributions Constructed from Copulas
mvdc | Multivariate Distributions Constructed from Copulas
mvdc-class | Class "mvdc": Multivariate Distributions from Copulas

## -- N --

nac2list | Constructing (Outer) Nested Archimedean Copulas
nacFrail.time | Timing for Sampling Frailties of Nested Archimedean Copulas
nacopula | Constructing (Outer) Nested Archimedean Copulas
nacopula-class | Class "nacopula" of Nested Archimedean Copulas
nacPairthetas | Pairwise Thetas of Nested Archimedean Copulas
nesdepth | Nesting Depth of a Nested Archimedean Copula ("nacopula")
normalCopula | Construction of Elliptical Copula Class Objects
normalCopula-class | Class "ellipCopula" of Elliptical Copulas
nParam | Fix a Subset of a Copula Parameter Vector
nParam-method | Fix a Subset of a Copula Parameter Vector

## -- O --

onacopula | Constructing (Outer) Nested Archimedean Copulas
onacopulaL | Constructing (Outer) Nested Archimedean Copulas
opower | Outer Power Transformation of Archimedean Copulas
optimMeth | Fitting Copulas to Data - Copula Parameter Estimation
outer_nacopula-class | Class "nacopula" of Nested Archimedean Copulas

## -- P --

P2p | Tools to Work with Matrices
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
pairsColList | Plots for Graphical GOF Test via Pairwise Rosenblatt Transforms
pairsRosenblatt | Plots for Graphical GOF Test via Pairwise Rosenblatt Transforms
pairwiseCcop | Computations for Graphical GOF Test via Pairwise Rosenblatt Transforms
pairwiseIndepTest | Computations for Graphical GOF Test via Pairwise Rosenblatt Transforms
parCopula-class | Mother Classes "Copula", etc of all Copulas in the Package
pCopula | Density, Evaluation, and Random Number Generation for Copula Functions
pcopula | Density, Evaluation, and Random Number Generation for Copula Functions
pCopula-method | Density, Evaluation, and Random Number Generation for Copula Functions
pCopula-method | Construction of Elliptical Copula Class Objects
pCopula-method | Evaluation of (Nested) Archimedean Copulas
persp-method | Methods for Function 'persp' in Package 'copula'
persp-methods | Methods for Function 'persp' in Package 'copula'
pK | Kendall Distribution Function for Archimedean Copulas
plackettCopula | Construction of a Plackett Copula
plackettCopula-class | Class "plackettCopula" of Plackett Copulas
plot-method | Methods for 'plot' in Package 'copula'
plot-methods | Methods for 'plot' in Package 'copula'
pMvdc | Multivariate Distributions Constructed from Copulas
pmvdc | Multivariate Distributions Constructed from Copulas
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
prob-method | Computing Probabilities of Hypercubes
prob-methods | Computing Probabilities of Hypercubes
psi | Generator Functions for Archimedean and Extreme-Value Copulas
psi-method | Generator Functions for Archimedean and Extreme-Value Copulas
psi-methods | Generator Functions for Archimedean and Extreme-Value Copulas
pSibuya | Sibuya Distribution - Sampling and Probabilities
psiDabsMC | Absolute Value of Generator Derivatives via Monte Carlo
pviTest | Computations for Graphical GOF Test via Pairwise Rosenblatt Transforms

## -- Q --

qacR | Distribution of the Radial Part of an Archimedean Copula
qK | Kendall Distribution Function for Archimedean Copulas
qqplot2 | Q-Q Plot with Rugs and Pointwise Asymptotic Confidence Intervals

## -- R --

radSymTest | Test of Exchangeability for a Bivariate Copula
rAntitheticVariates | Variance-Reduction Methods
rCopula | Density, Evaluation, and Random Number Generation for Copula Functions
rcopula | Density, Evaluation, and Random Number Generation for Copula Functions
rCopula-method | Density, Evaluation, and Random Number Generation for Copula Functions
rdj | Daily Returns of Three Stocks in the Dow Jones
retstable | Sampling Exponentially Tilted Stable Distributions
retstableR | Sampling Exponentially Tilted Stable Distributions
rF01Frank | Sample Univariate Distributions Involved in Nested Frank and Joe Copulas
rF01Joe | Sample Univariate Distributions Involved in Nested Frank and Joe Copulas
rFFrank | Sampling Distribution F for Frank and Joe
rFJoe | Sampling Distribution F for Frank and Joe
rho | Dependence Measures for Bivariate Copulas
rho-method | Dependence Measures for Bivariate Copulas
rho-method | Class '"mixCopula"' of Copula Mixtures
rho-methods | Dependence Measures for Bivariate Copulas
rK | Kendall Distribution Function for Archimedean Copulas
rLatinHypercube | Variance-Reduction Methods
rlog | Sampling Logarithmic Distributions
rlogR | Sampling Logarithmic Distributions
rMvdc | Multivariate Distributions Constructed from Copulas
rmvdc | Multivariate Distributions Constructed from Copulas
rnacModel | Random nacopula Model
rnacopula | Sampling Nested Archimedean Copulas
rnchild | Sampling Child 'nacopula's
rotCopula | Construction and Class of Rotated aka Reflected Copulas
rotCopula-class | Construction and Class of Rotated aka Reflected Copulas
rSibuya | Sibuya Distribution - Sampling and Probabilities
rSibuyaR | Sibuya Distribution - Sampling and Probabilities
RSpobs | Pseudo-Observations of Radial and Uniform Part of Elliptical and Archimedean Copulas
rstable | Random numbers from (Skew) Stable Distributions
rstable1 | Random numbers from (Skew) Stable Distributions
rtrafo | Conditional Distributions and Their Inverses from Copulas

## -- S --

safeUroot | One-dimensional Root (Zero) Finding - Extra "Safety" for Convenience
serialIndepTest | Serial Independence Test for Continuous Time Series Via Empirical Copula
serialIndepTestSim | Serial Independence Test for Continuous Time Series Via Empirical Copula
setTheta | Specify the Parameter(s) of a Copula
setTheta-method | Specify the Parameter(s) of a Copula
show-method | Class "acopula" of Archimedean Copula Families
show-method | Class "interval" of Simple Intervals
show-method | Class "mvdc": Multivariate Distributions from Copulas
show-method | Print Compact Overview of a Nested Archimedean Copula ("nacopula")
show-method | Methods for 'show()' in Package 'copula'
show-methods | Methods for 'show()' in Package 'copula'
Sibuya | Sibuya Distribution - Sampling and Probabilities
sinc | Sinc, Zolotarev's, and Other Mathematical Utility Functions
SMI.12 | SMI Data - 141 Days in Winter 2011/2012
spearmansRho | Dependence Measures for Bivariate Copulas
splom2 | Methods for Scatter Plot Matrix 'splom2' in Package 'copula'
splom2-method | Methods for Scatter Plot Matrix 'splom2' in Package 'copula'
splom2-methods | Methods for Scatter Plot Matrix 'splom2' in Package 'copula'
Stirling1 | Eulerian and Stirling Numbers of First and Second Kind
Stirling1.all | Eulerian and Stirling Numbers of First and Second Kind
Stirling2 | Eulerian and Stirling Numbers of First and Second Kind
Stirling2.all | Eulerian and Stirling Numbers of First and Second Kind
Summary-method | Class "interval" of Simple Intervals
summary-method | Classes of Fitted Multivariate Models: Copula, Mvdc
summaryFitCopula-class | Classes of Fitted Multivariate Models: Copula, Mvdc
summaryFitMvdc-class | Classes of Fitted Multivariate Models: Copula, Mvdc

## -- T --

tailIndex | Dependence Measures for Bivariate Copulas
tau | Dependence Measures for Bivariate Copulas
tau-method | Dependence Measures for Bivariate Copulas
tau-methods | Dependence Measures for Bivariate Copulas
tauAMH | Ali-Mikhail-Haq ("AMH")'s and Joe's Kendall's Tau
tauJoe | Ali-Mikhail-Haq ("AMH")'s and Joe's Kendall's Tau
tawnCopula | Construction of Extreme-Value Copula Objects
tawnCopula-class | Classes Representing Extreme-Value Copulas
tCopula | Construction of Elliptical Copula Class Objects
tCopula-class | Class "ellipCopula" of Elliptical Copulas
tevCopula | Construction of Extreme-Value Copula Objects
tevCopula-class | Classes Representing Extreme-Value Copulas
toEmpMargins | The Empirical Copula

## -- U --

upfhCopula | Construction of Fréchet-Hoeffding Bound Copula Objects
upfhCopula-class | Class "fhCopula" of Fréchet-Hoeffding Bound Copulas
uranium | Uranium Exploration Dataset of Cook & Johnson (1986)

## -- V --

vcov.fittedMV | Estimation of Multivariate Models Defined via Copulas

## -- W --

wireframe2 | Perspective Plots via 'wireframe2'
wireframe2-method | Perspective Plots via 'wireframe2'
wireframe2-methods | Perspective Plots via 'wireframe2'

## -- X --

Xcopula-class | Mother Classes "Copula", etc of all Copulas in the Package
xcopula-class | Mother Classes "Copula", etc of all Copulas in the Package
xvCopula | Model (copula) selection based on 'k'-fold cross-validation

## -- misc --

%in%-method | Class "interval" of Simple Intervals
.ac.classNames | Get "acopula" Family Object by Name
.ac.longNames | Get "acopula" Family Object by Name
.ac.objNames | Get "acopula" Family Object by Name
.ac.shortNames | Get "acopula" Family Object by Name
.emle | Maximum Likelihood Estimators for (Nested) Archimedean Copulas
.pairsCond | Pairs Plot of a cu.u Object (Internal Use)