copula (version 0.99-4)

archmCopula: Construction of Archimedean copula class object

Description

Constructs an Archimedean copula class object with its corresponding parameter and dimension.

Usage

archmCopula(family, param, dim = 2, ...)
claytonCopula(param, dim = 2)
frankCopula(param, dim = 2)
gumbelCopula(param, dim = 2)
amhCopula(param, dim = 2)

Arguments

family

a character string specifying the family of an Archimedean copula. Implemented families are "clayton", "frank", and "gumbel".

param

a numeric vector specifying the parameter values.

dim

the dimension of the copula.

...

currently nothing.

Value

• An Archimedean copula object of class "claytonCopula", "frankCopula", "gumbelCopula", or "amhCopula".

Details

archmCopula() is a wrapper for claytonCopula(), frankCopula(), gumbelCopula() and amhCopula().

Only the bivariate Ali-Mikhail-Haq copula family ("amhCopula") is available.

The maximum dimension for which the expression of the pdf is available is 6 for the Clayton, Gumbel and Frank families. The cdf expression is always available.

The maximum dimension for which "dcopula" can be evaluated is 10 for the Clayton and Gumbel families, and 6 for the Frank family. They are also the maximum dimensions for which maximum likelihood estimation can be done.

It is now recommended to work with the acopula-classed Archimedean copulas, as there is now restriction on the dimension there.

References

R.B. Nelsen (2006), An introduction to Copulas, Springer, New York.

See Also

ellipCopula, evCopula.

acopula-classed Archimedean copulas, such as copClayton, copGumbel, etc.

Examples

clayton.cop <- claytonCopula(2, dim = 3)
## scatterplot3d(rcopula(clayton.cop, 1000))

frank.cop <- frankCopula(3)
persp(frank.cop, dcopula)

gumbel.cop <- archmCopula("gumbel", 5)
contour(gumbel.cop, dcopula)

amh.cop <- amhCopula(0.5)


## A 7-dim Frank copula
frank.cop <- frankCopula(3, dim = 7)
x <- rcopula(frank.cop, 5)
## dcopula doesn't work
dcopula(frank.cop, x)

## A 7-dim Gumbel copula
gumbel.cop <- gumbelCopula(2, dim = 7)
## the expression of the pdf is not available
gumbel.cop@exprdist
## but can still be evaluated
dcopula(gumbel.cop, x)