# ArchimedeanCopulae: 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:

 `rarchmCopula` Generates Archimedean copula variates, `parchmCopula` computes Archimedean copula probability, `darchmCopula` computes Archimedean copula density, `rarchmSlider` displays interactive plots of variates, `parchmSlider` displays interactive plots of probability, `darchmSlider` displays interactive plots of density.

Special Copulae Functions:

 `rgumbelCopula` Generates Gumbel copula variates, `pgumbelCopula` computes Gumbel copula probability, `dgumbelCopula` computes Gumbel copula density.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```rarchmCopula(n, alpha = NULL, type = archmList()) parchmCopula(u = 0.5, v = u, alpha = NULL, type = archmList(), output = c("vector", "list"), alternative = FALSE ) darchmCopula(u = 0.5, v = u, alpha = NULL, type = archmList(), output = c("vector", "list"), alternative = FALSE ) rarchmSlider(B = 10) parchmSlider(type = c("persp", "contour"), B = 10) darchmSlider(type = c("persp", "contour"), B = 10) rgumbelCopula(n, alpha = 2) pgumbelCopula(u = 0.5, v = u, alpha = 2, output = c("vector", "list")) dgumbelCopula(u = 0.5, v = u, alpha = 2, output = c("vector", "list")) ```

## Arguments

 `alpha` [Phi*][*archmCopula] - the parameter of the Archemedean copula. A numerical value. `alternative` [*Copula] - Should the probability be computed alternatively ... `B` [*Slider] - the maximum slider menu value when the boundary value is infinite. By default this is set to 10. `n` [rarchmCopula] - the number of random deviates to be generated, an integer value. `output` [*archmCopula] - output - a character string specifying how the output should be formatted. By default a vector of the same length as `u` and `v`. If specified as `"list"` then `u` and `v` are expected to span a two-dimensional grid as outputted by the function `grid2d` and the function returns a list with elements `\\$x`, `\\$y`, and `\\$z` which can be directly used for example by 2D plotting functions. `type` [*archmCopula] - the type of the Archimedean copula. A character string ranging beween `"1"` and `"22"`. By default copula No. 1 will be chosen. [*archmSlider] - the type of the plot. A charcter string either specifying a perspective or contour plot. `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`.

## 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 May 31, 2017, 3:40 a.m.