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

## Description

A collection and description of functions concerned with the generator function for the Archimedean copula and with functions for setting and checking the distributional parameters.

Functions:

 `evList` Returns list of implemented Archimedean copulae, `archmParam` Sets default parameters for an Archimedean copula, `archmRange` returns the range of valid rho values, `archmCheck` checks if rho is in the valid range, `Phi` Computes generator Phi, inverse and derivatives, `PhiSlider` displays interactively generator function, `Kfunc` computes copula density and its inverse, `KfuncSlider` displays interactively density function.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```archmList() archmParam(type = archmList()) archmRange(type = archmList(), B = Inf) archmCheck(alpha, type = archmList()) Phi(x, alpha = NULL, type = archmList(), inv = FALSE, deriv = paste(0:2)) PhiSlider(B = 5) Kfunc(x, alpha = NULL, type = archmList(), inv = FALSE, lower = 1.0e-8) KfuncSlider(B = 5) ```

## Arguments

 `alpha` [Phi*][*archmCopula] - the parameter of the Archemedean copula. A numerical value. `B` [archmRange] - the maximum slider menu value when the boundary value is infinite. By default this is set to `B=Inf`. [*Slider] - the maximum slider menu value when the boundary value is infinite. By default this is set to `B=5`. `deriv` [Phi] - an integer value. Should the function itself, `deriv="0"`, or the first `deriv="1"`, or second `deriv="2"` derivative be evaluated? `inv` [Phi][Kfunc] - a logical flag. Should the inverse function be computed? `lower` [Kfunc] - a numeric value setting the lower bound for the internal root finding function `uniroot`. `type` [*archmCopula][Phi][Kfunc] - the type of the Archimedean copula. A character string ranging beween `"1"` and `"22"`. By default copula No. 1 will be chosen. `x` [Kfunc] - a numeric value or vector ranging between zero and one. [Phi] - a numeric value or vector.

## Value

The function `Phi` returns a numeric vector with the values computed from the Archemedean generator, its derivatives, or its inverse.

The function `Kfunc` returns a numeric vector with the values of the density and inverse for Archimedian copulae.

## Author(s)

Diethelm Wuertz for the Rmetrics R-port.

## References

RB Nelson - An Introduction to Copulas

## Examples

 ```1 2 3 4``` ``` ## archmList - # Return list of implemented copulae: archmList() ```

fCopulae documentation built on May 31, 2017, 3:40 a.m.