lcopula

Liouville copulas

Various functions to estimate one of five Liouville copula families as defined in the copula package. Since the models only admit closed-form survival functions for the integer-valued cased, the optimization routine proceeds pointwise over grid values for the parameter alpha and optimizes over rho. The procedure is computationally intensive.

Possible functions of interest include

rliouv to generate from the Liouville copula, but also dliouv, pliouv for density and distribution function
dliouvm, sliouvm, isliouvm, pliouvm for marginals of the Liouville copulas
liouv.maxim to fit a copula model to data for some possible combinations of alpha. It is possible to rely on a Monte-Carlo approximation of the inverse survival function to speed up computations. This is the default and is heavily recommended
liouv.maxim.mm for method-of-moments based estimation: for the Gumbel and Clayton families, explicit formulas for Kendall's tau can be used to define a moment-based estimator
pickands.liouv and pickands.plot for the Pickands dependence function of extremal attractors of Liouville copulas (respectively the negative scaled Dirichlet when CDA="C" and positive scaled Dirichlet when CDA="S")
hbvevdliouv for the spectral densities of extremal attractors
liouv.Tau for the theoretical Kendall's tau value for a given set of parameters from the Gumbel or Clayton Liouville copulas
K.plot for Kendall dependence plots

Datasets

Three datasets, airquality, danube and nutrient are included with the package.

Installation

The package is available from CRAN. For up-to-date versions, you can install it from from Github via

devtools::install_github("lbelzile/lcopula")

after installing devtools.