Construction of Extreme-Value Copula Objects
Constructs an extreme-value copula class object with its corresponding parameter.
evCopula(family, param, dim = 2, ...) galambosCopula(param) huslerReissCopula(param) tawnCopula(param) tevCopula(param, df = 4, df.fixed = FALSE)
family |
a character string specifying the family of an
extreme-value copula. Currently implemented are
|
param |
a numeric vector specifying the parameter values. |
dim |
the dimension of the copula. Currently, only |
df |
a number specifying the degrees of freedom of the t
extreme-value copula, |
df.fixed |
logical; if true, the degrees of freedom will never be
considered as a parameter to be estimated; |
... |
currently nothing. |
An object of class "gumbelCopula",
"galambosCopula",
"huslerReissCopula",
"tawnCopula", or "tevCopula".
The Gumbel copula is both an Archimedean and an extreme-value copula,
with principal documentation on gumbelCopula (or
archmCopula).
## 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))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.