copula: Generic copulae definitions

In acopula: Modelling Dependence with Multivariate Archimax (or any User-Defined Continuous) Copulas

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_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.

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.

Author(s)

Tomas Bacigal

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)

acopula documentation built on Sept. 11, 2023, 1:08 a.m.