# 00fCopulae-package: Modelling Copulae and Dependence Structures In fCopulae: Rmetrics - Bivariate Dependence Structures with Copulae

## Description

The Rmetrics `fCopulae` package is a collection of functions to manage, to investigate and to analyze bivariate financial returns by Copulae. Included are the families of Archemedean, Elliptical, Extreme Value, and Empirical Copulae.

## Details

 Package: fCopulae Type: Package Version: R 3.0.1 Date: 2014 License: GPL Version 2 or later Copyright: (c) 1999-2014 Rmetrics Assiciation URL: https://www.rmetrics.org

## 1 Introduction

The package `fCoplae` was written to explore and investigate bivariate copulae and dependence structures.

## 2 Archimedean Copulae

This chapter contains functions for analysing and modeling Archemedean copulae.

Archimedean Copula Density, Probability and Random Numbers:

 ```1 2 3 4``` ``` darchmCopula Computes Archimedean copula density parchmCopula Computes Archimedean copula probability rarchmCopula Generates Archimedean copula random variates ```

For the Gumbel Copula we have a fast implementation.

 ```1 2 3 4``` ``` rgumbelCopula Generates fast gumbel random variates dgumbelCopula Computes bivariate Gumbel copula density pgumbelCopula Computes bivariate Gumbel copula probability ```

Archimedean Copula Dependency Structure:

 ```1 2 3``` ``` archmTau Returns Kendall's tau for Archemedean copulae archmRho Returns Spearman's rho for Archemedean copulae ```
 ```1 2 3``` ``` archmTailCoeff Computes tail dependence for Archimedean copulae archmTailPlot Plots Archimedean tail dependence function ```

Archimedean Copula Generator:

 ```1 2 3 4 5``` ``` archmList Returns list of implemented Archimedean copulae archmParam Sets Default parameters for an Archimedean copula archmRange Returns the range of valid alpha values archmCheck Checks if alpha is in the valid range ```
 ```1 2 3 4 5``` ``` Phi Computes Archimedean Phi, inverse and derivatives PhiSlider Displays interactively generator function Kfunc Computes Archimedean Density Kc and its Inverse KfuncSlider Displays interactively the density and concordance ```

Archemedean Copula Modeling:

 ```1 2 3``` ``` archmCopulaSim Simulates bivariate elliptical copula archmCopulaFit Fits the paramter of an elliptical copula ```

Archemedean Copula Slider:

 ```1 2 3 4``` ``` darchmSlider Displays interactively archimedean density parchmSlider Displays interactively Archimedean probability rarchmSlider Displays interactively Archimedean probability ```

## 3 Elliptical Copulae

This chapter contains functions for analysing and modeling elliptical copulae.

Elliptical Copula Density, Probability and Random Numbers:

 ```1 2 3 4``` ``` dellipticalCopula Computes elliptical copula density pellipticalCopula Computes elliptical copula probability rellipticalCopula Generates elliptical copula variates ```

Elliptical Copula Slider:

 ```1 2 3 4``` ``` dellipticalSlider Generates interactive plots of density pellipticalSlider Generates interactive plots of probability rellipticalSlider Generates interactive plots of random variates ```

Elliptical Copula Dependency Structures:

 ```1 2 3``` ``` ellipticalTau Computes Kendall's tau for elliptical copulae ellipticalRho Computes Spearman's rho for elliptical copulae ```
 ```1 2 3``` ``` ellipticalTailCoeff Computes tail dependence for elliptical copulae ellipticalTailPlot Plots tail dependence function ```

Elliptical Copula Generator:

 ```1 2 3 4 5``` ``` ellipticalList Returns list of implemented Elliptical copulae ellipticalParam Sets default parameters for an elliptical copula ellipticalRange Returns the range of valid rho values ellipticalCheck Checks if rho is in the valid range ```
 ```1 2 3``` ``` gfunc Generator function for elliptical distributions gfuncSlider Slider for generator, density and probability ```

Elliptical Copula Modeling:

 ```1 2 3``` ``` ellipticalCopulaSim Simulates bivariate elliptical copula ellipticalCopulaFit Fits the paramter of an elliptical copula ```

## 4 Extreme Value Copulae

This chapter contains functions for analysing and modeling extreme value copulae.

Extremem Value Copula Density, Probability and Random Numbers:

 ```1 2 3 4``` ``` devCopula Computes extreme value copula density pevCopula Computes extreme value copula probability revCopula Generates extreme value copula random variates ```
 ```1 2 3 4``` ``` devSlider Displays interactively plots of density pevSlider Displays interactively plots of probability revSlider isplays interactively plots of random variates ```

Extreme Value Copula Dependeny Structures:

 ```1 2 3``` ``` evTau Returns Kendall's tau for extreme value copulae evRho Returns Spearman's rho for extreme value copulae ```
 ```1 2 3``` ``` evTailCoeff Computes tail dependence for extreme value copulae evTailCoeffSlider Plots extreme value tail dependence function ```

Extreme Value Copula Generator:

 ```1 2 3 4 5``` ``` evList Returns list of implemented extreme value copulae evParam Sets Default parameters for an extreme value copula evCheck Checks if parameters are in the valid range evRange Returns the range of valid parameter values ```
 ```1 2 3``` ``` Afunc Computes Dependence function AfuncSlider Displays interactively dependence function ```

Extreme Value Copula Modeling:

 ```1 2 3``` ``` evCopulaSim Simulates bivariate extreme value copula evCopulaFit Fits the paramter of an extreme value copula ```

## 5 Empirical Copula.

This chapter contains functions for analysing and modeling empirical copulae.

Empirical Copulae Density and Probability:

 ```1 2 3``` ``` pempiricalCopula Computes empirical copula probability dempiricalCopula Computes empirical copula density ```

The `fCopulae` Rmetrics package is written for educational support in teaching "Computational Finance and Financial Engineering" and licensed under the GPL.