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\name{ArchimedeanGenerator}
\alias{ArchimedeanGenerator}
\alias{archmList}
\alias{archmParam}
\alias{archmRange}
\alias{archmCheck}
\alias{Phi}
\alias{PhiSlider}
\alias{Kfunc}
\alias{KfuncSlider}
\title{Bivariate Archimedean Copulae}
\description{
A collection and description of functions
concerned with the generator function for
the Archimedean copula and with functions
for setting and checking the distributional
parameters.
\cr
Functions:
\tabular{ll}{
\code{evList} \tab Returns list of implemented Archimedean copulae, \cr
\code{archmParam} \tab Sets default parameters for an Archimedean copula, \cr
\code{archmRange} \tab returns the range of valid rho values, \cr
\code{archmCheck} \tab checks if rho is in the valid range, \cr
\code{Phi} \tab Computes generator Phi, inverse and derivatives, \cr
\code{PhiSlider} \tab displays interactively generator function, \cr
\code{Kfunc} \tab computes copula density and its inverse, \cr
\code{KfuncSlider} \tab displays interactively density function. }
}
\usage{
archmList()
archmParam(type = archmList())
archmRange(type = archmList(), B = Inf)
archmCheck(alpha, type = archmList())
Phi(x, alpha = NULL, type = archmList(), inv = FALSE, deriv = paste(0:2))
PhiSlider(B = 5)
Kfunc(x, alpha = NULL, type = archmList(), inv = FALSE, lower = 1.0e-8)
KfuncSlider(B = 5)
}
\arguments{
\item{alpha}{
[Phi*][*archmCopula] - \cr
the parameter of the Archemedean copula. A numerical value.
}
\item{B}{
[archmRange] - \cr
the maximum slider menu value when the boundary value is infinite.
By default this is set to \code{B=Inf}.\cr
[*Slider] - \cr
the maximum slider menu value when the boundary value is infinite.
By default this is set to \code{B=5}.
}
\item{deriv}{
[Phi] - \cr
an integer value. Should the function itself, \code{deriv="0"},
or the first \code{deriv="1"}, or second \code{deriv="2"} derivative
be evaluated?
}
\item{inv}{
[Phi][Kfunc] - \cr
a logical flag. Should the inverse function be computed?
}
\item{lower}{
[Kfunc] - \cr
a numeric value setting the lower bound for the internal root
finding function \code{uniroot}.
}
\item{type}{
[*archmCopula][Phi][Kfunc] - \cr
the type of the Archimedean copula. A character string ranging
beween \code{"1"} and \code{"22"}. By default copula No. 1 will
be chosen.
}
\item{x}{
[Kfunc] - \cr
a numeric value or vector ranging between zero and one.\cr
[Phi] - \cr
a numeric value or vector.
}
}
\value{
The function \code{Phi} returns a numeric vector with the values
computed from the Archemedean generator, its derivatives, or its
inverse.
\cr
The function \code{Kfunc} returns a numeric vector with the
values of the density and inverse for Archimedian copulae.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\references{
RB Nelson - An Introduction to Copulas
}
\examples{
## archmList -
# Return list of implemented copulae:
archmList()
}
\keyword{models}
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