evCopula: Construction of Extreme-Value Copula Objects

In copula: Multivariate Dependence with Copulas

Construction of Extreme-Value Copula 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. Currently implemented are "galambos", "gumbel", "huslerReiss", "tawn", "tev".
param	a numeric vector specifying the parameter values.
dim	the dimension of the copula. Currently, only "gumbel" allows dim > 2.
df	a number specifying the degrees of freedom of the t extreme-value copula, tevCopula().
df.fixed	logical; if true, 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".

Note

The Gumbel copula is both an Archimedean and an extreme-value copula, with principal documentation on gumbelCopula (or archmCopula).

See Also

ellipCopula, archmCopula, gofEVCopula, An.

Examples

## Gumbel is both
stopifnot(identical(   evCopula("gumbel"), gumbelCopula()),
          identical(archmCopula("gumbel"), gumbelCopula()))

## For a given degree of dependence these copulas are strikingly similar :

tau <- 1/3

gumbel.cop      <- gumbelCopula     (iTau(gumbelCopula(),      tau))
galambos.cop    <- galambosCopula   (iTau(galambosCopula(),    tau))
huslerReiss.cop <- huslerReissCopula(iTau(huslerReissCopula(), tau))
tawn.cop        <- tawnCopula       (iTau(tawnCopula(),        tau))
tev.cop         <- tevCopula        (iTau(tevCopula(),         tau))

curve(A(gumbel.cop, x), 0, 1, ylab = "A(<cop>( iTau(<cop>(), tau)), x)",
      main = paste("A(x) for five Extreme Value cop. w/  tau =", format(tau)))
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, col=2, add=TRUE)# very close to Gumbel

## And look at the differences
curve(A(gumbel.cop, x) - A(tawn.cop, x), ylim = c(-1,1)*0.005,
      ylab = '', main = "A(<Gumbel>, x) - A(<EV-Cop.>, x)")
abline(h=0, lty=2)
curve(A(gumbel.cop, x) - A(galambos.cop, x), add=TRUE, col=2)
curve(A(gumbel.cop, x) - A(huslerReiss.cop, x), add=TRUE, col=3)
curve(A(gumbel.cop, x) - A(tev.cop, x), add=TRUE, col=4, lwd=2)


## the t-EV-copula has always positive tau :
curve(vapply(x, function(x) tau(tevCopula(x)), 0.), -1, 1,
      n=257, ylim=0:1, xlab=quote(rho),ylab=quote(tau),
      main= quote(tau( tevCopula(rho) )), col = 2, lwd = 2)
rect(-1,0,1,1, lty = 2, border = adjustcolor("black", 0.5))

copula documentation built on Sept. 11, 2024, 7:48 p.m.