acopula (version 0.9.4)

generator: Generator of Archimedean copula

Description

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

Usage

generator(name,...)
genAMH(...)
genClayton(...)
genFrank(...)
genGumbel(...)
genJoe(...)
genLog(...)

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

Arguments

name

character; code name for generator, identical with the part after 'gen'

...

named arguments; items of the generator definition list to be redefined

Author

Tomas Bacigal

Details

Currently implemented families of Archimedean copula generator:

family	generator \(\phi(t)=\)	\(p\)ar.range	Archimed.case
Ali-Mikhail-Haq	\(\log\left(\frac{1-(1-t)p}{t}\right)\)	[-1,1[	-1(\(\Pi\))
Clayton	\(t^(-p) - 1 \)	[0,Inf]	0(\(\Pi\)),Inf(M)
Frank	\(-\log\left( \frac{\exp(-p t)-1}{\exp(-p)-1} \right)\)	[-Inf,Inf]	-Inf(W),0(\(\Pi\)),Inf(M)
Gumbel-Hougaard	\((-\log(t))^{p}\)	[1,Inf]	1(\(\Pi\)),Inf(M)
Joe	\(-\log(1-(1-t)^p)\)	[1,Inf]	1(\(\Pi\)),Inf(M)
Log	\(-\log(t)\)		\(\Pi\)

References

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

See Also

pCopula, depfun, copula

Examples

## 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)