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.