Statistical Inference of Vine Copulas

Provides tools for the statistical analysis of vine copula models. The package includes tools for parameter estimation, model selection, simulation, goodness-of-fit tests, and visualization. Tools for estimation, selection and exploratory data analysis of bivariate copula models are also provided.

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Vine copulas are a flexible class of dependence models consisting of bivariate building blocks (see e.g., Aas et al., 2009). You can find a comprehensive list of publications and other materials on

This package is primarily made for the statistical analysis of vine copula models. The package includes tools for parameter estimation, model selection, simulation, goodness-of-fit tests, and visualization. Tools for estimation, selection and exploratory data analysis of bivariate copula models are also provided. Please see the API documentation for a detailed description of all functions.

Table of contents

How to install

You can install:

  • the stable release on CRAN:

  • the latest development version:


Package overview

Below, we list most functions and features you should know about. As usual in copula models, data are assumed to be serially independent and lie in the unit hypercube.

  • BiCop: Creates a bivariate copula by specifying the family and parameters (or Kendall's tau). Returns an object of class BiCop. The class has the following methods:

    • print, summary: a brief or comprehensive overview of the bivariate copula, respectively.

    • plot, contour: surface/perspective and contour plots of the copula density. Possibly coupled with standard normal margins (default for contour).

  • BiCopSim: Simulates from a bivariate copula.

  • BiCopEst: Estimates parameters of a bivariate copula with a prespecified family. Estimation can be done by maximum likelihood (method = "mle") or inversion of the empirical Kendall's tau (method = "itau", only available for one-parameter families). Returns an object of class BiCop.

  • BiCopSelect: Estimates the parameters of a bivariate copula for a set of families and selects the best fitting model (using either AIC or BIC). Returns an object of class BiCop.

  • BiCopGofTest: Goodness-of-Fit tests for bivariate copulas.

  • BiCopVuongClarke: Vuong and Clarke tests for model comparison within a prespecified set of copula families.

  • BiCopPar2Tau, BiCopTau2Par, BiCopPar2Beta, BiCopPar2TailDep: Conversion between dependence measures and parameters (for a given family). Functions are vectorized in all arguments.

  • Evaluate functions related to a bivariate copula: BiCopPDF, BiCopCDF, BiCopDeriv, BiCopDeriv2, BiCopHfunc, BiCopHfuncDeriv, BiCopHfuncDeriv2, BiCopHinv. Functions are vectorized in the family, par, and par2 arguments.

  • BiCopKDE: Kernel density plots for copula data.

  • BiCopLambda, BiCopKPlot, BiCopChiPlot: Further plot types for the analysis of bivariate copulas.

For most functions, you can provide an object of class BiCop instead of specifying family, par and par2 manually.

Vine copula modeling: the RVine-family

  • RVineMatrix: Creates a vine copula model by specifying structure, family and parameter matrices. Such matrices have been introduced by Dissman et al. (2013). Returns an object of class RVineMatrix. The class has the following methods:

    • plot: Plots the trees of the the R-vine tree structure. Optionally, you can annotate the edges with pair-copula families and parameters.

    • contour: Creates a matrix of contour plots associated with the pair-copulas.

  • RVineSim: Simulates from a vine copula model.

  • RVineSeqEst: Estimates the parameters of a vine copula model with prespecified structure and families.

  • RVineCopSelect: Estimates the parameters and selects the best family for a vine copula model with prespecified structure matrix.

  • RVineStructureSelect: Fits a vine copula model assuming no prior knowledge. It selects the R-vine structure using Dissmann et al. (2013)'s method, estimates parameters for various families, and selects the best family for each pair.

  • RVineGoFTest: Goodness-of-Fit tests for a vine copula model (c.f., Schepsmeier, 2013, 2015). Related functions are RVineGrad, RVineHessian, RVineStdError, and RVinePIT.

  • RVineVoungTest, RVineClarkeTest: Vuong and Clarke tests for comparing two vine copula models.

  • RVinePar2Tau, RVinePar2Beta: Calculate dependence measures corresponding to a vine copula model.

  • RVinePDF, RVineLogLik, RVineAIC, RVineBIC: Calculate the density, log-likelihood, AIC, and BIC of a vine copula.

Additional features

The functions C2RVine and D2RVine create RVineMatrix objects for C- and D-vine copulas. This is particularly useful for former users of the CDVine package.

Furthermore, bivariate and vine copula models from this packages can be used with the copula package (Hofert et al., 2015). For example, vineCopula transforms an RVineMatrix object into an object of class vineCopula which provides methods for dCopula, pCopula, and rCopula. For more details, we refer to the package manual.

Bivariate copula families

In this package several bivariate copula families are included for bivariate and multivariate analysis using vine copulas. It provides functionality of elliptical (Gaussian and Student-t) as well as Archimedean (Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7 and BB8) copulas to cover a large range of dependence patterns. For Archimedean copula families, rotated versions are included to cover negative dependence as well.

The Tawn copula is an asymmetric extension of the Gumbel copula with three parameters. For simplicity, we implemented two versions of the Tawn copula with two parameters each. Each type has one of the asymmetry parameters fixed to 1, so that the corresponding copula density is either left- or right-skewed (in relation to the main diagonal). In the manual we will call these two new copulas "Tawn type 1" and "Tawn type 2".

The following table shows the parameter ranges of bivariate copula families with parameters par and par2 and internal coding family:

Copula family family par par2
Gaussian 1 (-1, 1) -
Student t 2 (-1, 1) (2,Inf)
(Survival) Clayton 3, 13 (0, Inf) -
Rotated Clayton (90 and 270 degrees) 23, 33 (-Inf, 0) -
(Survival) Gumbel 4, 14 [1, Inf) -
Rotated Gumbel (90 and 270 degrees) 24, 34 (-Inf, -1] -
Frank 5 R \ {0} -
(Survival) Joe 6, 16 (1, Inf) -
Rotated Joe (90 and 270 degrees) 26, 36 (-Inf, -1) -
(Survival) Clayton-Gumbel (BB1) 7, 17 (0, Inf) [1, Inf)
Rotated Clayton-Gumbel (90 and 270 degrees) 27, 37 (-Inf, 0) (-Inf, -1]
(Survival) Joe-Gumbel (BB6) 8, 18 [1 ,Inf) [1, Inf)
Rotated Joe-Gumbel (90 and 270 degrees) 28, 38 (-Inf, -1] (-Inf, -1]
(Survival) Joe-Clayton (BB7) 9, 19 [1, Inf) (0, Inf)
Rotated Joe-Clayton (90 and 270 degrees) 29, 39 (-Inf, -1] (-Inf, 0)
(Survival) Joe-Frank (BB8) 10, 20 [1, Inf) (0, 1]
Rotated Joe-Frank (90 and 270 degrees) 30, 40 (-Inf, -1] [-1, 0)
(Survival) Tawn type 1 104, 114 [1, Inf) [0, 1]
Rotated Tawn type 1(90 and 270 degrees) 124, 134 (-Inf, -1] [0, 1]
(Survival) Tawn type 2 204, 214 [1, Inf) [0, 1]
Rotated Tawn type 2 (90 and 270 degrees) 224, 234 (-Inf, -1] [0, 1]

Associated shiny apps


This small shiny app enables the user to draw nice tree plots of an R-Vine copula model using the package d3Network. Models have to be set up locally in an RVineMatrix object and uploaded as .RData file. The page is still under construction.
Author: Ulf Schepsmeier


Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182-198.

Bedford, T. and R. M. Cooke (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial intelligence 32, 245-268.

Bedford, T. and R. M. Cooke (2002). Vines - a new graphical model for dependent random variables. Annals of Statistics 30, 1031-1068.

Brechmann, E. C., C. Czado, and K. Aas (2012). Truncated regular vines in high dimensions with applications to financial data. Canadian Journal of Statistics 40 (1), 68-85.

Brechmann, E. C. and C. Czado (2011). Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Statistics & Risk Modeling, 30 (4), 307-342.

Brechmann, E. C. and U. Schepsmeier (2013). Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine. Journal of Statistical Software, 52 (3), 1-27.

Czado, C., U. Schepsmeier, and A. Min (2012). Maximum likelihood estimation of mixed C-vines with application to exchange rates. Statistical Modelling, 12(3), 229-255.

Dissmann, J. F., E. C. Brechmann, C. Czado, and D. Kurowicka (2013). Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59 (1), 52-69.

Eschenburg, P. (2013). Properties of extreme-value copulas Diploma thesis, Technische Universitaet Muenchen

Hofert, M., I. Kojadinovic, M. Maechler, and J. Yan (2015). copula: Multivariate Dependence with Copulas. R package version 0.999-13

Joe, H. (1996). Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In L. Rueschendorf, B. Schweizer, and M. D. Taylor (Eds.), Distributions with fixed marginals and related topics, pp. 120-141. Hayward: Institute of Mathematical Statistics.

Joe, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman and Hall.

Knight, W. R. (1966). A computer method for calculating Kendall's tau with ungrouped data. Journal of the American Statistical Association 61 (314), 436-439.

Kurowicka, D. and R. M. Cooke (2006). Uncertainty Analysis with High Dimensional Dependence Modelling. Chichester: John Wiley.

Kurowicka, D. and H. Joe (Eds.) (2011). Dependence Modeling: Vine Copula Handbook. Singapore: World Scientific Publishing Co.

Nelsen, R. (2006). An introduction to copulas. Springer

Nagler, T. (2015). kdecopula: Kernel Smoothing for Bivariate Copula Densities. R package version 0.6.0.

Schepsmeier, U. and J. Stoeber (2012). Derivatives and Fisher information of bivariate copulas. Statistical Papers, 55 (2), 525-542.

Schepsmeier, U. (2013) A goodness-of-fit test for regular vine copula models. Preprint.

Schepsmeier, U. (2015) Efficient information based goodness-of-fit tests for vine copula models with fixed margins. Journal of Multivariate Analysis 138, 34-52.

Stoeber, J. and U. Schepsmeier (2013). Estimating standard errors in regular vine copula models. Computational Statistics, 28 (6), 2679-2707

White, H. (1982) Maximum likelihood estimation of misspecified models, Econometrica, 50, 1-26.


VineCopula 2.1.7 (September 17, 2018)


  • prevent heap-buffer overflows in BiCopHfuncDeriv(2) (non-critical).

VineCopula 2.1.7 (August 31, 2018)


  • get rid of warning messages when checking whether structure is a D-vine.

  • fix standard errors for one-parameter families.

  • avoid infinite loop for Joe's inverse h-function with extreme parameter values.

  • fix parameters bounds for BB copulas in RVineMLE().

VineCopula 2.1.6 (June 18, 2018)


  • fix rotation handling in derivative calculations.

  • fix check for whether a structure is a D-vine.

  • fixed typos in API documentation.

VineCopula 2.1.5 (May 16, 2018)


  • no family restrictions for RVinePIT.


  • fix calculation of Kendall's tau when joint ties are present.

  • fix missing pair.AIC/BIC in RVineSeqEst().

  • improved starting parameter for Joe copula MLE.

VineCopula 2.1.4 (February 11, 2018)


  • All C-headers are now located in inst/include/VineCopula (#48).

  • Most C routines are registered as C-callable (#47).


  • RVineMLE can now safely called with only independence copulas (#49).

  • Fixed fix (non-critical) memory-access bug.

VineCopula 2.1.3 (August 15, 2017)


  • summary.RVineMatrix() invisibly returns a data.frame containg most of what is printed as output.

  • Less restrictive conditions on what is considered an appropriate treecrit function in RVineStructureSelect() (thanks to Thibault Vatter, #40).

  • New option verbose in RVinePDF() (thanks to @cag51, #36).


  • Fix parameter bounds in RVineMLE() corresponding to updated requirements in BiCop-functions.

  • Adapt to re-naming of tailIndex to lambda in the copula package (thanks to Benedikt Graeler, #41, #42).

  • Fix bug in detecting C-vine copulas for summary/print.RVineMatrix() (#38).

VineCopula 2.1.2 (April 24, 2017)



  • Fixed bug in preprocessing of weights argument.

  • More informative error message when family is unknown.

  • Safer BiCopSelect() with presel = TRUE and insufficient data.

  • Fixed RVineMatrix() (output dimension was d-1 and naturalOrder = TRUE wasn't working, thanks @tvatter).

  • Safer BiCopEst() for method = "itau".

VineCopula 2.1.1 (January 11, 2017)


  • Package now requires copula (>= 0.999-16). The new version of copula requires VineCopula to be re-installed, because the old fitCopula() method doesn't work any longer, but was re-exported by VineCopula.


  • Package developers can use the VineCopula C-functionality by linking against VineCopula through the LinkingTo field.

VineCopula 2.1.0 (December 23, 2016)


  • Now depends explicitly on R (>= 3.1.0). So far, this dependence was implicit trhough our dependence on the copula package.


  • All estimation functions now have a method argument. The default is method = "mle" and corresponds to the old behavior. The other option, method = "itau", estimates the parameters by inversion of Kendall's. It is much faster than method = "mle", but is only available for one-parameter families and the t-copula. Big thanks to Thibault Vatter who did most of the work (PR #25).

  • New function RVineMatrixSample that randomly generates valid R-vine matrices using the algorithm of Joe et al. (2011). Contributed by Thibault Vatter (PR #27).

  • Faster versions of RVineMatrix and RVineCopSelect, and RVineStructureSelect by avoiding unnecessary computations (thanks to Thibault Vatter, PRs #29 and #31).

  • All -Select functions now have a presel argument. If TRUE (default) the familyset is reduced to families that have asymmetry charactistics that conform with the observed data.

  • RVineSim, RVineLogLik, and RVinePDF have been implemented in a way that demands less memory. For RVineLogLik, the option calculate.V has to be set to TRUE.


  • Fixed bug in upper tail dependence coefficient for survival BB1 (reported by Viviana Fernandez, thanks!).

  • RVineStructureSelect now works in dimension two as well.

  • RVineMatrixCheck returns the new error code -4 when the matrix is neither lower nor upper triangular (threw an actual error before).

  • contour.RVineMatrix now arranges the contour matrix conforming with the family and parameter matrices.

VineCopula 2.0.5 (September 25, 2016)


  • Require higher version of the copula package (>= 0.999-15).


  • Use se = FALSE as default throughout the package for faster estimation.

  • Fixed errors in BiCopGofTest for the Student t copula and par2 close to 2 and for most other families for tau close to 0 (reported by Thong Huy Nguyen, thanks!).

  • Fix sign in starting parameters for Tawn MLE.

  • Fixed storage positions of par2 in output matrix of RVineMLE (reported by Robin Evans, thanks!).

VineCopula 2.0.4 (August 8, 2016)


  • Option for kernel contours in contour.RVineMAtrix.


  • Return scalar instead of 1-dim array in tau <-> par conversion.

  • Fix vectorized call of BiCopCDF.

  • Negative selection of families is now working properly.

  • Correct logLik calculation in output of RVineMLE.

  • Dependence measures are updated in output of RVineCor2pcor.

  • Fix bug in annotation of edges with Kendall's when using plot.RVineMatrix.

VineCopula 2.0.1 (June 9, 2016)


  • fixed small memory leak (reported by Prof. Ripley, thanks!).

VineCopula 2.0.0 (June 8, 2016)



  • igraph has been removed from Imports.

  • network has been added to Imports.


  • All functions in the package can now handle NAs in the data. A warning message indicates presence of NAs and explains how they are treated.

  • Extend BiCop and RVineMatrix objects (now include: associated dependence measures; fit statistics and p-values, if available).

  • New methods print and summary for objects of class BiCop and RVineMatrix.

  • New plotting generics:

    • plot.RVineMatrix for plotting vine trees,

    • contour.RVineMatrix for a matrix of contour plots,

    • contour.BiCop as short hand for plot.BiCop(..., type = "contour").

  • Vectorize BiCopXyz-functions w.r.t. family, par, par2:

    • in C: BiCopPDF, BiCopHfunc, BiCopHinv, BiCopDeriv, BiCopDeriv2, BiCopHfuncDeriv, BiCopHfuncDeriv2.

    • in R: BiCopCDF, BiCopPar2Tau, BiCopPar2Beta, BiCopPar2TailDep.

  • Etimation of vine copulas (RVineStructureSelect, RVineCopSelect, RVineSeqEst) can now be done in parallel using the cores argument (based on foreach) and is more memory efficient (pseudo-observations are discarded as soon they are useless).

  • RVineStructureSelect now takes an argument treecrit allowing for several preimplemented (and custom) choices of the edge weight used in Dissmann's algorithm.

  • Treatment of familyset in the -Select functions:

    • independence copula is handled as a regular family,

    • negative integers can be used to select from all but a subset of families.

  • New function BiCopCompare: A shiny app where the user can visually assess how well several families fit the data.

  • New function BiCopKDE for kernel density plots (based on kdecopula package).

  • New function BiCopCondSim for conditional simulation from a bivariate copula.

  • New function BiCopHinv for computation of inverse h-functions.

  • New functions BiCopHfunc1, BiCopHfunc2, BiCopHinv1, and BiCopHinv2 that only compute one of the two h-functions (or inverse h-functions).

  • New function BiCopCheck for checking of family/parameter consistency.

  • Add argument to the above functions for the option to omit family/parameter consistency checks (for internal usage). When FALSE, the Clayton and Frank copulas can be used with par = 0.

  • Faster implementations of BiCopPar2Tau/BiCopTau2Par for Frank copula and BiCopTau2Par conversion for Joe copula.


  • Correct call for non-t families in BiCopHfuncDeriv2(..., deriv = "par1u2").

  • The S4-class objets of the Tawn copulas pointed to Archimedean CDFs, now corrected to true CDFs based on C-code.

  • TauMatrix: restriction for input data to be in [0,1] removed.

  • RVineCopSelect: no printing of family matrix.

  • Added methods for Pickand's dependence function "A" for tawnT1Copula, surTawnT1Copula, tawnT2Copula and surTawnT2Copula.

  • Use C-code instead of R-code and remove redundant C-code of Tawn copulas.

  • Small bug fix in log-likelihood for families 3, 4, 7, 17.

  • Increased upper limit for uniroot in

  • Fixed rotations of Tawns (they were actually reflection w.r.t. the axes u = 0.5 and u2 = 0.5)

  • Correct calculation of the goodness-of-fit test based on Whites Information matrix test for bivariate copulas BiCopGofTest(..., method = "white"). The variance matrix needed for the test statistic had a poor approximation. Thereby the asymptotic p-values are corrected.

  • Bound parameter ranges for Archimedean copulas to avoid numerical instabilities in -PDF and -Sim functions.

VineCopula 1.6-1 (November 9, 2015)


  • Removed CDVine from Suggests.


  • Fix code/documentation mismatch in function 'pobs' following a change in the copula package.

VineCopula 1.6 (July 16, 2015)


  • RVineTreePlot: option for a legend (and numbered nodes and edges).


  • Definition of "C" in BiCopCDF for tawn copulas used constants u1 and u2 instead of arguments u and v.

  • RVineStructureSelect: Adjust to new version of igraph. Tree structure was not selected correctly. igraph function names changed to the names used in the new version. Some small modifications to avoid some for loops and make the code easier to read.


  • Extend Imports to avoid undefined globals (CRAN E-mail 02.07.2015).

  • New version requires igraph (>= 1.0.0).

VineCopula 1.5 (June 2, 2015)


  • as.copuladata: coerce to class copuladata.

  • pairs.copuladata: pairs plots for objects of class copuladata.

  • RVinePDF: PDF of an R-Vine Copula Model.

  • BiCopSelect, RVineCopSelect, RVineStructureSelect: add option rotations = TRUE which augments the familyset with all rotations to a given family.

  • RVineMatrix, RVineStructureSelect: allow upper triangular matrices as input (output remains lower triangular).

  • BiCop objects for bivariate copulas:

  • add constructor BiCop and plotting generic plot.BiCop.

  • define results of BiCopEst/BiCopSelect as BiCop objects.

  • add compatibility with other BiCopXyz functions (BiCopPDF, BiCopPar2Tau, etc.).


  • BiCopEst: extend search interval for Tawn MLE to avoid optim-errors.

  • BiCopEst: fix for optim error ('non-finite value supplied').

  • RVineSim: reorder U so that it corresponds to the order of RVM.

  • RVineCor2pcor: include normalization step for a more intuitive behavior, bug fix for $d = 2, 3$ and $d > 9$.

  • RVinePcor2cor: bug fixes for $d = 2$ and $d > 9$.

  • RVineCopSelect: RVM object now uses variable names as provided by data.

VineCopula 1.4 (January 26, 2015)


  • BiCopTau2Par and BiCopPar2Tau: fully vectorized (parameter/tau input), and sanity checks extended. Before vector input was not prohibited. However, both functions were not intended to be used for vectorized input.

VineCopula 1.3-2 (January 19, 2015)


  • Thomas Nagler


  • Import/Export of function 'pobs' from 'copula' package.


  • RVineStructureSelect: Bug concerning the dimensions of input data/security queries fixed (Reported by Sarka Cerna, Radek Solnicky and Ludovic Theate. Thanks a lot!)

  • RVineStructureSelect: Correct handling of rotated BBs and Tawns.

  • BiCopSelect, BiCopEst: Improved starting values for Tawn MLE.

  • hfunc.c:

    • Correct Hfunc1 for Tawns.

    • Bound all results to lie in 0,1

    • Extension of Hinv1 and Hinv2 in analogy to Hfunc1 and Hfunc2.

  • incompleteBeta.c: Misuse of the C function abs (as reported by CRAN) corrected to fabs.

  • gof_PIT.R: Use of require() replaced by requireNamespace according to 'Writing R Extensions'.

  • Package ADGofTest removed from Suggests (see 'Writing R Extensions' for usage of Suggests).

  • Import of function ad.test from ADGofTest for gof_PIT.R.

VineCopula 1.3-1 (September 10, 2014)


  • Bootstrap procedure for the White test (RVineGofTest, gof_White) was incorrect. (Reported by Piotr Zuraniewski and Daniel Worm. Thanks!)

  • Bootstrap procedure for the PIT based and the ECP based test were incorrect. First, C starts to count at 0 not 1. This could result in zero entries in the bootstrapped data matrix. Second, forget to permute vdirect and vindirect according to the permutation of data.

  • BiCopSelect: For the rotated BB7 and BB8 (family = 37, 38) the limiting cases were incorrect for very small parameters (copy&paste error). (Reported by Radek Solnicky. Thanks!)

VineCopula 1.3 (March 26, 2014)


VineCopula 1.2-1 (March 21, 2014)


  • Added tests generated from example code.


  • Moved copula from Depends to the more appropriate Import field.

VineCopula 1.2-1 (March 4, 2014)


  • RVineSim allows to commit a (N x d)-matrix of $U[0,1]$ random variates to be transformed to the copula sample. For example if you want to use quasi random variables instead of the pseudo random variables implemented in R. (Thanks to Marius Hofert)

  • The package now contains class wrappers that are compatible with the copula class from the copula R-package. These include all bivariate families currently implemented: The class representation for different rotated families of e.g the BB6 family are represented as BB6Copula, r90B6Copula, surBB6Copula and r270BB6Copula. These bivariate classes are fully compatible with the standard copula methods such as dCopula, pCopula, rCopula or fitCopula including persp and contour. A vine copula can as well be coerced into a class representation of vineCopula. However, the support of the standard methods is limited. See the corresponding help pages for details. Earlier introduced R-wrapper of C-functions have been removed, as they are no longer needed by the spcopula R-package.

  • Added parameter verbose to RVineLogLik to allow to suppress some debug output.


  • RVineMLE: the optim argument parscale was not correctly defined for all cases.

  • RVineAIC/RVineBIC: Instead of the function arguments par and par2 the calculation was based on RVM$par and RVM$par2. This is corrected now. (reported by Marcel Duellmann; thanks)

  • RVineStructureSelect: The new igraph version returned a different variable type causing an error in the second and higher order tree selection.

VineCopula 1.2 (October 09, 2013)


  • RVinePIT: calculation of the probability integral transform (PIT) for R-vines.

  • RVineGofTest: 15 different goodness-of-fit tests for R-vine copulas (Schepsmeier 2013).

  • print.RVM: A more detailed summary is printed if print(RVM, detail = TRUE) is set.

  • BetaMatrix: Matrix of empirical Blomqvist's beta values.

  • BiCopPar2Beta: Blomqvist's beta value of a bivariate copula.

  • RVinePar2Beta: Blomqvist's beta values of an R-vine copula model.

  • RVineCor2pcor: correlations to partial correlations for R-vines.

  • RVinePcor2cor: partial correlations to correlations for R-vines.

  • New copula families for most of the BiCop as well as for the RVine-functions:

  • As an asymmetric extension of the Gumbel copula, the Tawn copula with three parameters is now also included in the package. Both the Gumbel and the Tawn copula are extreme-value copulas, which can be defined in terms of their corresponding Pickands dependence functions.

  • For simplicity, we implemented two versions of the Tawn copula with two parameters each. Each type has one of the asymmetry parameters fixed to 1, so that the corresponding Pickands dependence is either left- or right-skewed. In the manual we will call these two new copulas "Tawn type 1" and "Tawn type 2".

  • The families 104, 114, 124, 134 denote the Tawn copula and their rotated versions in the case of left skewness (Tawn type 1).

  • The families 204, 214, 224, 234 denote the Tawn copula and their rotated versions in the case of right skewness (Tawn type 2).


  • BiCopPar2Tau: corrected calculation of Kendall's tau of rotated BB7. (Reported by Giampiero Marra. Thanks!)

  • RVineStructureSelect: Corrected code for the igraph package.

  • RVineTreePlot: Now a 3-dimensional R-vine can be plotted too.

  • Corrected upper tail dependence coefficient for the survival BB1 copula (BiCopPar2TailDep).

  • Minor improvement in BiCopSelect regarding the starting values for parameter estimation.


  • Updated manual files.

VineCopula 1.1-2 (July 09, 2013)


  • Benedikt Graeler


  • Changed dependency from igraph0 to igraph since the support for igraph0 will be quit soon.

  • Additional validity check of the R-vine matrix in RVineMatrix (Code provided by Harry Joe). Also available as separate function RVineMatrixCheck.

  • New bivariate copula: Reflection asymmetric Archimedean copula. In our functions it is family = 41, 51, 61, 71 ( with rotated versions). So far only implemented in some bivariate functions (not documented so far; experimental).


  • New (correct) examples for the Clarke and Vuong test.

  • Fixed memory problem in the C-function ktau (TauMatrix).

VineCopula 1.1-1 (February 7, 2013)


  • Fixed issue with the inverse h-function of the Gumbel copula.

VineCopula 1.1 (February 4, 2013)


  • BiCopGofTest: Goodness-of-fit test for bivariate copulas based on White's information matrix equality as introduced by Wanling and Prokhorov (2011). The formally included function BiCopGofKendall is now part of BiCopGofTest (method = "kendall").

  • Additional edge label pair in RVineTreePlot to display the indices of the (conditioned) pairs of variables identified by the edges.

  • In RVineStructureSelect and RVineCopSelect a truncation level can be set.

  • Improved inverse h-functions for the Gumbel and Joe copulas (thanks to Harry Joe).

  • C to R wrapping functions for the h-functions (Hfunc1, Hfunc2), the bivariate log-likelihood function (LL_mod_seperate), the bivariate Archimedean copula CDF (archCDF) and the simulation function for C- and D-vines (pcc) (request of Benedikt Graeler for the R-package spcopula).

  • The functions R2CVine and R2Dine were removed, since they were only correct in special cases.


  • Work around for a problem with optim and the analytical gradient in BiCopEst.

  • Improvement of the bivariate maximum likelihood estimation (BiCopEst).

  • In the functions BiCopCDF and BiCopGoFTest(..., method = "Kendall") the t-copula is not implemented any more. The calculation of the CDF was incorrect for non-integer values of the degrees-of-freedom parameter. The implemented algorithm in the mvtnorm package only works for integer values of the degrees-of-freedom parameter.

  • Improvement in the calculation of the cdf of the Frank copula (BiCopCDF).

Reference manual

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2.1.8 by Thomas Nagler, 5 months ago

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Browse source code at

Authors: Ulf Schepsmeier [aut] , Jakob Stoeber [aut] , Eike Christian Brechmann [aut] , Benedikt Graeler [aut] , Thomas Nagler [aut, cre] , Tobias Erhardt [aut] , Carlos Almeida [ctb] , Aleksey Min [ctb, ths] , Claudia Czado [ctb, ths] , Mathias Hofmann [ctb] , Matthias Killiches [ctb] , Harry Joe [ctb] , Thibault Vatter [ctb]

Documentation:   PDF Manual  

Task views: Probability Distributions

GPL (>= 2) license

Imports graphics, grDevices, stats, utils, MASS, mvtnorm, network, methods, copula, kdecopula, ADGofTest, lattice, doParallel, parallel, foreach

Suggests CDVine, TSP, shiny, testthat, numDeriv

Imported by AssetCorr, CDVineCopulaConditional, GJRM, OpVaR, gamCopula, gofCopula, kdevine, pacotest.

Suggested by copula, kdecopula.

See at CRAN