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\name{ExtremeValueCopulae}
\alias{ExtremeValueCopulae}
\alias{revCopula}
\alias{pevCopula}
\alias{devCopula}
\alias{revSlider}
\alias{pevSlider}
\alias{devSlider}
\title{Bivariate Extreme Value Copulae}
\description{
A collection and description of functions to investigate
bivariate extreme value copulae.
\cr
Extreme Value Copulae Functions:
\tabular{ll}{
\code{revCopula} \tab Generates extreme value copula random variates, \cr
\code{pevCopula} \tab computes extreme value copula probability, \cr
\code{devCopula} \tab computes extreme value copula density, \cr
\code{revSlider} \tab displays interactive plots of extreme value random variates, \cr
\code{pevSlider} \tab displays interactive plots of extreme value probability, \cr
\code{devSlider} \tab displays interactive plots of extreme value density. }
}
\usage{
revCopula(n, param = NULL, type = evList())
pevCopula(u = 0.5, v = u, param = NULL, type = evList(),
output = c("vector", "list"), alternative = FALSE )
devCopula(u = 0.5, v = u, param = NULL, type = evList(),
output = c("vector", "list"), alternative = FALSE )
revSlider(B = 10)
pevSlider(type = c("persp", "contour"), B = 10)
devSlider(type = c("persp", "contour"), B = 10)
}
\arguments{
\item{alternative}{
[evRho][evTau][*evCopula] - \cr
Should the probability be computed alternatively in a
direct way from the probability formula or by default
via the dependency function?
}
\item{B}{
[*Slider] - \cr
the maximum slider menu value when the boundary value is
infinite. By default this is set to 10.
}
%\item{error}{
% [evRho] - \cr
% the error bound to be achieved by the \code{integrate2d}
% integration formula. A numeric value, by default \code{error=1.0e-5}.
% }
\item{n}{
[revCopula][evCopulaSim] - \cr
the number of random deviates to be generated, an integer value.
}
\item{output}{
[*evCopula] - \cr
output - a character string specifying how the output should
be formatted. By default a vector of the same length as
\code{u} and \code{v}. If specified as \code{"list"}
then \code{u} and \code{v} are
expected to span a two-dimensional grid as outputted by the
function \code{grid2d} and the function returns a list with
elements \code{$x}, \code{y}, and \code{z} which can be directly
used for example by 2D plotting functions.
}
\item{param}{
[*ev*][A*] - \cr
distribution and copulae parameters.
A numeric value or vector of named parameters as required by
the copula specified by the variable \code{type}.
If set to \code{NULL}, then the default parameters will be taken.
}
\item{type}{
[*ev*][Afunc] - \cr
the type of the extreme value copula. A character
string selected from: "gumbel", "galambos", "husler.reiss",
"tawn", or "bb5".
\cr
[evSlider] - \cr
a character string specifying the plot type. Either a
perspective plot which is the default or a contour plot
with an underlying image plot will be created.
}
\item{u, v}{
[*evCopula][*archmCopula] - \cr
two numeric values or vectors of the same length at which
the copula will be computed. If \code{u} is a list then the
the \code{$x} and \code{$y} elements will be used as \code{u}
and \code{v}. If \code{u} is a two column matrix then the
first column will be used as \code{u} and the the second
as \code{v}.
}
}
\value{
The function \code{pcopula} returns a numeric matrix of probabilities
computed at grid positions \code{x}|\code{y}.
\cr
The function \code{parchmCopula} returns a numeric matrix with values
computed for the Archemedean copula.
\cr
The function \code{darchmCopula} returns a numeric matrix with values
computed for thedensity of the Archemedean copula.
\cr
The functions \code{Phi*} return a numeric vector with the values
computed from the Archemedean generator, its derivatives, or its
inverse.
\cr
The functions \code{cK} and \code{cKInv} return a numeric vector with the
values of the density and inverse for Archimedian copulae.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## fCOPULA -
getClass("fCOPULA")
getSlots("fCOPULA")
## revCopula -
# Not yet implemented
# revCopula(n = 10, type = "galambos")
## pevCopula -
pevCopula(u = grid2d(), type = "galambos", output = "list")
## devCopula -
devCopula(u = grid2d(), type = "galambos", output = "list")
## AfuncSlider -
# Generator, try:
\dontrun{AfuncSlider()}
}
\keyword{models}
|
