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\name{Tail Correlation Functions}
\alias{tcf}
\alias{tail correlation functions}
\alias{Tail correlation functions}
\alias{RMmodelsTailCorrelation}
\title{Covariance models valid for max-stable random fields}
\description{
This page summarizes the models that can be used
for tail correlation functions.
}
\details{
The following models are available:
\bold{Completely monotone functions allowing for arbitrary scale}
\tabular{ll}{
\command{\link{RMbcw}} \tab Model bridging stationary and
intrinsically stationary processes for \code{alpha <= 1}
and \code{beta < 0}\cr
\command{\link{RMdagum}} \tab Dagum model with \eqn{\beta < \gamma}
and \eqn{\gamma \le 1}\cr
\command{\link{RMexp}} \tab exponential model \cr
\command{\link{RMgencauchy}} \tab generalized Cauchy family with
\eqn{\alpha \le 1} (and arbitrary \eqn{\beta> 0})\cr
\command{\link{RMmatern}} \tab Whittle-Matern model with
\eqn{\nu \le 1/2}\cr
%multiquadric todo
%sine power todo
\command{\link{RMstable}} \tab symmetric stable family or powered
exponential model with \eqn{\alpha \le 1}\cr
\command{\link{RMwhittle}} \tab Whittle-Matern model, alternative
parametrization with \eqn{\nu \le 1/2}\cr
}
\bold{Other isotropic models with arbitrary scale}
\tabular{ll}{
\command{\link{RMnugget}} \tab nugget effect model \cr
}
\bold{Compactly supported covariance functions}
\tabular{ll}{
\command{\link{RMaskey}} \tab Askey's model\cr
\command{\link{RMcircular}} \tab circular model\cr
\command{\link{RMconstant}}\tab identically constant \cr
\command{\link{RMcubic}} \tab cubic model\cr
\command{\link{RMgengneiting}} \tab Wendland-Gneiting model;
differentiable models with compact support \cr
\command{\link{RMgneiting}} \tab differentiable model with compact
support \cr
\command{\link{RMspheric}} \tab spherical model \cr
}
\bold{Anisotropic models}
\tabular{ll}{
None up to now.
}
\bold{Basic Operators}
\tabular{ll}{
\command{\link{RMmult}}, \code{*} \tab product of covariance models \cr
\command{\link{RMplus}}, \code{+} \tab sum of covariance models or variograms\cr
}
\bold{Operators related to process constructions}
\tabular{ll}{
\command{\link{RMbernoulli}} \tab correlation of binary fields\cr
\command{\link{RMbrownresnick}}\tab tcf of a \link{Brown-Resnick} process\cr
\command{\link{RMschlather}}\tab tcf of an extremal Gaussian
process / \link[=RMschlather]{Schlather} process \cr
\command{\link{RMm2r}}\tab M2 process with monotone shape function\cr
\command{\link{RMm3b}}\tab M3 process with balls of random radius\cr
\command{\link{RMmps}}\tab M3 process with hyperplane polygons\cr
% \command{\link{}}\tab \cr
}
\bold{See \link{RMmodels} for cartesian models.}
}
\references{
\itemize{
\item
Strokorb, K., Ballani, F., and Schlather, M. (2015)
Tail correlation functions of max-stable processes: Construction
principles, recovery and diversity of some mixing max-stable processes
with identical TCF. \emph{Extremes}, \bold{18}, 241-271
}
}
\me
\seealso{
\link{coordinate systems},
\link{RM},
\command{\link{RMmodels}},
\command{\link{RMtrafo}}.
}
\keyword{spatial}
\keyword{models}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
RFgetModelNames(type="tail")
## an example of a simple model
model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget
plot(model)
\dontshow{FinalizeExample()}}
|
