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\name{EllipticalGenerator}
\alias{EllipticalGenerator}
\alias{ellipticalList}
\alias{ellipticalParam}
\alias{ellipticalRange}
\alias{ellipticalCheck}
\alias{gfunc}
\alias{gfuncSlider}
\title{Bivariate Elliptical Copulae}
\description{
A collection and description of functions
concerned with the generator function for
the elliptical copula and with functions
for setting and checking the distributional
parameters.
\cr
Functions:
\tabular{ll}{
\code{ellipticalList} \tab Returns list of implemented elliptical copulae, \cr
\code{ellipticalParam} \tab Sets default parameters for an elliptical copula, \cr
\code{ellipticalRange} \tab returns the range of valid rho values, \cr
\code{ellipticalCheck} \tab checks if rho is in the valid range, \cr
\code{gfunc} \tab Generator function for elliptical distributions, \cr
\code{gfuncSlider} \tab Slider for generator, density and probability. }
}
\usage{
ellipticalList()
ellipticalParam(type = ellipticalList())
ellipticalRange(type = ellipticalList())
ellipticalCheck(rho = 0.75, param = NULL, type = ellipticalList())
gfunc(x, param = NULL, type = ellipticalList())
gfuncSlider(B = 10)
}
\arguments{
\item{B}{
[*Slider] - \cr
the maximum slider menu value when the boundary value is infinite.
By default this is set to 10.
}
\item{rho}{
[*ellipticalCopula] - \cr
is the numeric value setting the correlation strength, ranging
between minus one and one.
}
\item{param}{
[*ellipticalCopula][gfunc] - \cr
additional distributional parameters: for the Sudent-t distribution
this is "nu", for the Kotz distribution this is "r", and for the
Exponential Power distribution these are "r" and "s". If the
argument \code{param=NULL} then default values are taken. These are
for the Student-t \code{param=c(nu=4))}, for the Kotz distribution
\code{param=c(r=1))}, and for the exponential power distribution
\code{param=c(r=1,s=1)}. Note, that the Kotz and exponential power
copulae are independent of \code{r}, and that \code{r} only enters
the generator, the density, the probability and the quantile
functions.
}
\item{type}{
[*ellipticalCopula][gfunc] - \cr
the type of the elliptical copula. A character string selected
from: "norm", "cauchy", "t", "logistic", "laplace", "kotz",
or "epower".
[*ellipticalSlider] - \cr
a character string which indicates what kind of plot should be
displayed, either a perspective plot if \code{type="persp"}, the
default value, or a contour plot if \code{type="contour"}.
}
\item{x}{
[gfunc] - \cr
a numeric value or vector out of the range \code{[0,Inf)} at
which the generator will be computed.
}
}
\value{
\bold{Copula Functions:}
\cr\cr
The functions \code{[rpd]ellipticalCopula} return a numeric vector
of random variates, probabilities, or densities for the specified
copula computed at grid coordinates \code{u}|\code{v}.
\cr
The functions \code{[rpd]ellipticalSlider} display an interactive
graph of an perspective copula plot either for random variates,
probabilities or densities. Alternatively, an image underlayed
contour plot can be shown.
\cr
\bold{Copula Dependence Measures:}
\cr\cr
The functions \code{ellipticalTau} and \code{ellipticalRho} return
a numericc value for Kendall's Tau and Spearman's Rho.
\cr
\bold{Copula Tail Coefficient:}
\cr\cr
The function \code{ellipticalTailCoeff} returns the coefficient of
tail dependence for a specified copula. The function
\code{ellipticalTailPlot} displays a whole plot for the upper or
alternatively for the lower tail dependence as a function of
\code{u} for a set of nine \code{rho} values.
\cr
\bold{Copula Generator Function:}
\cr\cr
The function \code{gfunc} computes the generator function for the
specified copula, by default the normal copula. If the argument
\code{x} is missing, then the normalization constand lambda will
be returned, otherwise if \code{x} is specified the values for the
function \emph{g(x)} will be freturned. The selected type of copula
is added to the output as an attribute named \code{"control"}.
The function \code{gfuncSlider} allows to display interactively
the generator function, the marginal density, the marginal
probability, and the contours of the the bivariate density.
\cr
\bold{Copula Simulation and Parameter Fitting:}
\cr\cr
The function \code{ellipticalCopulaSim} returns a numeric two-column
matrix with randomly generated variates for the specified copula.
\cr
The function \code{ellipticalCopulaFit} returns a fit to empirical
data for the specified copula. The returned object is a list with
elements from the function \code{nlminb}.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## ellipticalList -
# List implemented copulae:
ellipticalList()
## gfunc -
# Generator Function:
gfunc(x <- (0:10)/10, param = 2, type = "t")
## gfuncSlider -
# Try:
\dontrun{
gfuncSlider()}
}
\keyword{models}
|
