copula (version 0.999-15)

evCopula: Construction of Extreme-Value Copula Class Objects

Description

Constructs an extreme-value copula class object with its corresponding parameter.

Usage

evCopula(family, param, dim = 2, ...)
galambosCopula(param)
huslerReissCopula(param)
tawnCopula(param)
tevCopula(param, df = 4, df.fixed = FALSE)

Arguments

family

a character string specifying the family of an extreme-value copula.

param

a numeric vector specifying the parameter values.

dim

the dimension of the copula.

df

a numerical value specifying the number of degrees of freedom the t extreme-value copula.

df.fixed

TRUE means that the degrees of freedom will never be considered as a parameter to be estimated; FALSE means that df will be estimated if the object is passed as argument to fitCopula.

...

currently nothing.

Value

An object of class "gumbelCopula", "galambosCopula", "huslerReissCopula", "tawnCopula", or "tevCopula".

See Also

ellipCopula, archmCopula, gofEVCopula, An.

Examples

## Notice that, for a given degree of dependence,
## these copulas are strikingly similar.

tau <- 0.33

gumbel.cop <- evCopula("gumbel")
stopifnot(identical(gumbel.cop, gumbelCopula()))
gumbel.cop@parameters <- iTau(gumbel.cop, tau)

galambos.cop <- galambosCopula()
galambos.cop@parameters <- iTau(galambos.cop, tau)

huslerReiss.cop <- huslerReissCopula()
huslerReiss.cop@parameters <- iTau(huslerReiss.cop, tau)

tawn.cop <- tawnCopula()
tawn.cop@parameters <- iTau(tawn.cop, tau)

tev.cop <- tevCopula()
tev.cop@parameters[1] <- iTau(tev.cop, tau)

curve(A(gumbel.cop, x), 0, 1,
      main = "A(x) for five Extreme Value cop. w/  tau = 1/3")
curve(A(galambos.cop, x), lty=2, add=TRUE)
curve(A(huslerReiss.cop, x), lty=3, add=TRUE)
curve(A(tawn.cop, x), lty=4, add=TRUE)
curve(A(tev.cop, x), lty=5, add=TRUE)

## the t-EV-copula has always positive tau :
curve(vapply(x, function(x) tau(tevCopula(x)), 0.), -1, 1,
      col=2, n=257, ylim=0:1, ylab=bquote(tau), xlab=bquote(rho),
      main= expression(tau( tevCopula(rho) )))