# ArchimedeanModelling: Bivariate Archimedean Copulae In fCopulae: Rmetrics - Bivariate Dependence Structures with Copulae

## Description

A collection and description of functions to investigate bivariate Archimedean copulae.

Archimedean Copulae Functions:

 `archmCopulaSim` simulates an Archimedean copula, `archmCopulaFit` fits the parameters of an Archimedean copula.

## Usage

 ```1 2``` ```archmCopulaSim(n, alpha = NULL, type = archmList()) archmCopulaFit(u, v = NULL, type = archmList(), ...) ```

## Arguments

 `alpha` [Phi*][*archmCopula] - the parameter of the Archemedean copula. A numerical value. `n` [rarchmCopula] - the number of random deviates to be generated, an integer value. `type` the type of the Archimedean copula. A character string ranging beween `"1"` and `"22"`. By default copula No. 1 will be chosen. `u, v` [*archmCopula] - two numeric values or vectors of the same length at which the copula will be computed. If `u` is a list then the the `\\$x` and `\\$y` elements will be used as `u` and `v`. If `u` is a two column matrix then the first column will be used as `u` and the the second as `v`. `...` [archmCopulaFit] - arguments passed to the optimization function in use, `nlminb`.

## Value

The function `pcopula` returns a numeric matrix of probabilities computed at grid positions `x`|`y`.

The function `parchmCopula` returns a numeric matrix with values computed for the Archemedean copula.

The function `darchmCopula` returns a numeric matrix with values computed for thedensity of the Archemedean copula.

The functions `Phi*` return a numeric vector with the values computed from the Archemedean generator, its derivatives, or its inverse.

The functions `cK` and `cKInv` return a numeric vector with the values of the density and inverse for Archimedian copulae.

## Author(s)

Diethelm Wuertz for the Rmetrics R-port.

fCopulae documentation built on Nov. 17, 2017, 2:31 p.m.