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\name{CopulaClass}
\alias{CopulaClass}
\alias{fCOPULA}
\alias{fCOPULA-class}
\alias{show,fCOPULA-method}
\alias{pfrechetCopula}
\title{Bivariate Copula Class}
\description{
A collection and description of functions to specify the
copula class and to investigate bivariate Frechet copulae.
\cr
The class representation and methods are:
\tabular{ll}{
\code{fCOPULA} \tab representation for an S4 object of class "fCOPULA", \cr
\code{show} \tab S4 print method. }
Frechet Copulae:
\tabular{ll}{
\code{pfrechetCopula} \tab computes Frechet copula probability. }
}
\usage{
\S4method{show}{fCOPULA}(object)
pfrechetCopula(u = 0.5, v = u, type = c("m", "pi", "w"),
output = c("vector", "list"))
}
\arguments{
\item{object}{
[show] - \cr
an S4 object of class \code{"fCOPULA"}.
}
\item{output}{
[*frechetCopula] - \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{$x}, \code{y}, and \code{z} which can be directly
used for example by 2D plotting functions.
}
\item{type}{
[*frechetCopula] - \cr
the type of the Frechet copula. A character
string selected from: \code{"m"}, \code{"pi"}, or \code{"w"}.
}
\item{u, v}{
two numeric values or vectors of the same length at which
the copula will be computed. If \code{u} is a list then the
the \code{$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 print method \code{show} returns an S4 object of
class \code{"fCOPULA"}. The object contains the following slots:
\item{@call}{
the function call.
}
\item{@copula}{
the name of the copula.
}
\item{@param}{
a list whose elements specify the model parameters of the
copula.
}
\item{@title}{
a character string with the name of the copula. This can be
overwritten specifying a user defined input argument.
}
\item{@description}{
a character string with an optional user defined description.
By default just the current date will be returned.
}
The function \code{pfrechetCopula} returns a numeric vector of
probabilities. An attribute named \code{"control"} is added
which returns the name of the Frechet copula.
}
\details{
The function \code{pfrechetCopula} returns a numeric matrix of
probabilities computed at grid positions \code{u}|\code{v}. The
arguments \code{u} and \code{v} are two single values or two
numeric vectors of the same length. If \code{v} is not specified
then the same values are taken as for \code{u}. Alternatively,
\code{u} may be given as a two column vector or as a list with
two entries as vectors. The first column or entry is taken as
\code{u} and the second as \code{v}.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## fCOPULA -
getClass("fCOPULA")
## pfrechet -
# The Frechet Copula - m:
pfrechetCopula(0.5)
pfrechetCopula(0.25, 0.75)
pfrechetCopula(runif(5))
## grid2d -
grid2d()
pfrechetCopula(grid2d())
}
\keyword{models}
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