# generator: Generator of Archimedean copula In acopula: Modelling dependence with multivariate Archimax (or any user-defined continuous) copulas.

## Description

Produce a list containing generator of specified Archimedean family, its inverse and derivatives with parameters bounds.

## Usage

 ```1 2 3 4 5 6 7 8``` ```generator(name,...) genAMH(...) genClayton(...) genFrank(...) genGumbel(...) genJoe(...) genLog(...) ```

## Arguments

 `name` character; code name for generator, identical with the part after 'gen' `...` named arguments; items of the generator definition list to be redefined

## Details

Currently implemented families of Archimedean copula generator:

 family generator φ(t)= par.range Archimed.case Ali-Mikhail-Haq log([1-(1-t)p]/t) [-1,1[ -1(Π) Clayton t^(-p) - 1 [0,Inf] 0(Π),Inf(M) Frank -log[(exp(-p t)-1)/(exp(-p)-1)] [-Inf,Inf] -Inf(W),0(Π),Inf(M) Gumbel-Hougaard (-log(t))^p [1,Inf] 1(Π),Inf(M) Joe -log(1-(1-t)^p) [1,Inf] 1(Π),Inf(M) Log -log(t) Π

## Value

 `parameters` numeric vector to be used whenever parameters of generator are not supplied to procedure that use it, or as starting values in estimation. `gen` function of two arguments. The first is generator argument, the another is genereator parameters. `gen.der` function. Generator first derivative. `gen.der2` function. Generator second derivative. `gen.inv` function. Generator inverse. `gen.inv.der` function. First derivative of generator inverse. `gen.inv.der2` function. second derivative of generator inverse. `kendall,spearman` list. Correlation coefficient as function of copula parameter (`coef`), its inverse (`icoef`) and range (`bounds`). Available only for 1-parameter families. `lower,upper` numeric; parameters boundary `id` character; identification of generator family

Tomas Bacigal

## References

Nelsen, R. B.: An introduction to copulas. Springer (2006).

## See Also

`pCopula`, `depfun`, `copula`

## Examples

 ```1 2 3 4 5 6``` ```## the following gives the same definition list genGumbel() generator("Gumbel") ## any list item can be modified upon function call genGumbel(parameters=2.2,upper=10) ```

acopula documentation built on May 30, 2017, 5:48 a.m.