copula (version 0.999-7)

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) )))