# copula: Generic copulae definitions In acopula: Modelling dependence with multivariate Archimax (or any user-defined continuous) copulas.

## Description

Produce a list containing CDF and/or PDF of an copula with parameters bounds.

## Usage

 ```1 2 3 4 5 6 7``` ```copula(name,...) copFGM(...) copGumbel(...) copNormal(dim=2,...) copPlackett(...) copProduct(...) ```

## Arguments

 `name` character. Code name for copula, identical with the part after `cop`. `dim` integer. Copula dimension. `...` named arguments. Items of the copula definition list to be redefined. Argument names must NOT be cropped.

## Details

Currently implemented copula families:

 family CDF C(t)= par.range special cases Farlie-Gumbel-Morgenstern prod(t)*(p*prod(1-t)+1) [-1,1] 0(Π) Gumbel-Hougaard exp(-sum((-log(t))^p)^(1/p)) [1,Inf] 1(Π),Inf(M) normal Φ_P(Φ^-1(t_1),...) ]-1,1[ -1(W),0(Π),1(M) Plackett (A-sqrt(A^2-4*prod(t)*p*(p-1)))/(2*(p-1)); A=1+(p-1)*sum(t) [0,Inf] 0(W),1(Π),Inf(M) product prod(t) Π

where Φ^-1 is quantile function of standard normal and Φ_P is CDF of multivariate normal distribution with correlation matrix P containing copula parameters.

## Value

 `parameters` numeric vector to be used whenever parameters of copula are not supplied to procedure that use it, or as starting values in estimation. `pcopula,dcopula` function of two arguments. The first is vector of copula arguments, the another is vector of parameters. `rcopula` function of two arguments. The first is copula dimension or length of random sample (normal copula), the another is vector of parameters. `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 copula family.

Tomas Bacigal

## References

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

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