# ArchimedeanDependency: 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:

 `archmTau` Computes Kendall's tau for Archimedean copulae, `archmRho` computes Spearman's rho for Archimedean copulae, `archmTailCoeff` computes tail dependence for Archimedean copulae, `archmTailPlot` plots tail dependence for Archimedean copulae.

## Usage

 ```1 2 3 4 5 6 7``` ``` archmTau(alpha = NULL, type = archmList(), lower = 1.0e-10) archmRho(alpha = NULL, type = archmList(), method = c("integrate2d", "adapt"), error = 1.0e-5) archmTailCoeff(alpha = NULL, type = archmList()) archmTailPlot(alpha = NULL, type = archmList(), tail = c("Upper", "Lower")) ```

## Arguments

 `alpha` the parameter of the Archemedean copula. A numerical value. `error` [archmRho] - the error bound to be achieved by the `integrate2d` integration formula. A numeric value, by default `error=1.0e-5`. `lower` [archmTau] - a numeric value setting the lower bound for the internal integration function `integrate`. `tail` [archmTailPlot] - a character string, either `"Upper"` or `"Lower"` denoting which of the two tails should be displayed. By default the upper tail dependence will be considered. `type` the type of the Archimedean copula. A character string ranging beween `"1"` and `"22"`. By default copula No. 1 will be chosen. `method` [archmRho] - a character string that determines which integration method should be used, either `"integrate2d"` or `"adapt"`. If the second method is selected the contributed R package `"adapt"` is required.

## 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.