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 | 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 |
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.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 |
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 |
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.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" |
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" |
htrafo | GOF Testing Transformation of Hering and Hofert |
huslerReissCopula | Construction of Extreme-Value Copula Objects |
huslerReissCopula-class | Classes Representing Extreme-Value Copulas |
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 |
joeCopula | Construction of Archimedean Copula Class Object |
joeCopula-class | Class "archmCopula" |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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) |
vcov.fittedMV | Estimation of Multivariate Models Defined via Copulas |
wireframe2 | Perspective Plots - 'wireframe2' in Package 'copula' |
wireframe2-method | Perspective Plots - 'wireframe2' in Package 'copula' |
wireframe2-methods | Perspective Plots - 'wireframe2' in Package 'copula' |
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 |
%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) |