acopula (version 0.9.4)

copula: 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(...)

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.

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.

Author

Tomas Bacigal

Details

Currently implemented copula families:

family	CDF \(C(t)=\)	\(p\)ar.range	special cases
Farlie-Gumbel-Morgenstern	\(\prod_i t_i (p\prod_i(1-t)+1)\)	[-1,1]	0(\(\Pi\))
Gumbel-Hougaard	\(\exp((-\sum_i(-\log t_i)^p)^{1/p})\)	[1,Inf]	1(\(\Pi\)),Inf(M)
normal	\(\Phi_P(\Phi^{-1}(t_1),...)\)	]-1,1[	-1(W),0(\(\Pi\)),1(M)
Plackett	\(\frac{A-\sqrt{A^2-4\prod_i t_ip(p-1)}}{2(p-1)}; A=1+(p-1)\sum_i t_i\)	[0,Inf]	0(W),1(\(\Pi\)),Inf(M)
product	\(-\prod_i t_i\)		\(\Pi\)

where \(\Phi^{-1}\) is quantile function of standard normal and \(\Phi_P\) is CDF of multivariate normal distribution with correlation matrix \(P\) containing copula parameters.

References

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

See Also

pCopula, generator, depfun

Examples

## 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)