https://github.com/lbelzile/lcopula

Liouville copulas
https://github.com/lbelzile/lcopula

copula extremes

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Liouville copulas

• Host: GitHub
• URL: https://github.com/lbelzile/lcopula
• Owner: lbelzile
• License: gpl-3.0
• Created: 2016-07-29T13:26:54.000Z (almost 10 years ago)
• Default Branch: main
• Last Pushed: 2025-10-22T09:27:51.000Z (8 months ago)
• Last Synced: 2025-12-09T12:39:03.834Z (6 months ago)
• Topics: copula, extremes
• Language: R
• Size: 3.04 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# lcopula

[![CRAN_Status_Badge](https://www.r-pkg.org/badges/version-last-release/lcopula)](https://cran.r-project.org/package=lcopula)

[![License](https://img.shields.io/badge/license-GPL%20%28%3E=%203%29-blue.svg?style=flat)](http://www.gnu.org/licenses/gpl-3.0.html) 

[![Downloads](http://cranlogs.r-pkg.org/badges/lcopula?color=brightgreen)](http://www.r-pkg.org/pkg/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

```R

devtools::install_github("lbelzile/lcopula")

```

after installing `devtools`.