copula {acopula} R Documentation

## Generic copulae definitions

### Description

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

### Usage

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.