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This package implements several functions for the estimation of meta-elliptical copulas and for the estimation of elliptical and trans-elliptical distributions:
elliptical distributions are distributions for which the isodensity surfaces/curves are ellipses. Their distribution is determined by a mean, a variance matrix and a univariate function called the generator.
(meta-)elliptical copulas are copulas defined implicitly as copula functions of elliptical distributions. Their distribution is determined by a correlation matrix and a generator.
trans-elliptical distributions are distributions whose copula is meta-elliptical and whose margins are arbitrary. In other words, a trans-elliptical distribution is a multivariate distribution built from the dependence structure (copula) of an elliptical distribution, but which could have any margin. Their distribution is therefore determined by the marginal distributions, the correlation matrix and the generator.
The release version on CRAN:
install.packages("ElliptCopulas")
The development version from GitHub:
# install.packages("remotes")
::install_github("AlexisDerumigny/ElliptCopulas") remotes
Inference of Elliptical Distributions
EllDistrEst
: nonparametric estimation of the
generator of an elliptical distribution.
EllDistrSim
: simulate data from an elliptical
distribution with a given arbitrary generator.
Inference of (Meta-)Elliptical Copulas
EllCopEst
: nonparametric estimation of the generator
of an elliptical copula.
EllCopSim
: simulate data from an elliptical copula
with a given arbitrary generator.
EllCopLikelihood
: compute the likelihood of a given
elliptical copula generator.
Inference of Trans-Elliptical Distributions
TEllDistrEst
: estimation of the marginal cdfs,
estimation of the correlation matrix by inversion of Kendall’s tau and
nonparametric estimation of the generator.Numerical analysis
DensityGenerator.normalize
: normalize an elliptical
copula density generator in order to satisfy the identifiability
constraints.
DensityGenerator.check
: check whether a given
density generator is normalized.
Convert_gd_To_g1
, Convert_g1_To_Fg1
,
Convert_g1_To_Qg1
, Convert_g1_To_f1
,
Convert_gd_To_fR2
: convert between
Derumigny, A., & Fermanian, J. D. (2022). Identifiability and estimation of meta-elliptical copula generators. Journal of Multivariate Analysis, article 104962. doi:10.1016/j.jmva.2022.104962, arXiv:2106.12367.
Liebscher, E. (2005). A semiparametric density estimator based on elliptical distributions. Journal of Multivariate Analysis, 92, 205–225. doi:10.1016/j.jmva.2003.09.007
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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