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\name{RMmodel}
\alias{RMmodel}
\alias{RMmodels}
\alias{[,RMmodel,ANY,ANY-method} %]
\alias{[<-,RMmodel,ANY,ANY-method} %]
\title{Covariance and Variogram Models in \pkg{RandomFields} (RM commands)}
\description{
Summary of implemented covariance and variogram models% in \link{RFformula}
}
\details{
To generate a covariance or variogram model for use within
\pkg{RandomFields}, calls of the form
\deqn{RM_name_(..., var, scale, Aniso, proj)}
can be used,
where _name_ has to be replaced by a valid model name.
\itemize{
\item
\code{...} can take model specific arguments. %Argument
%corresponding to specific covariance model
\item
\code{var} is the optional variance argument \eqn{v},
\item
\code{scale} the optional scale argument \eqn{s},
\item
\code{Aniso} an optional anisotropy matrix \eqn{A} or given by \command{\link{RMangle}}, and
\item
\code{proj} is the optional projection.
}
With \eqn{\phi} denoting the original model, the transformed model is
\eqn{C(h) = v * \phi(A*h/s)}.
See \command{\link{RMS}} for more details.
\command{RM_name_} must be a function of class
\command{\link[=RMmodelgenerator-class]{RMmodelgenerator}}.
The return value of all functions \command{RM_name_} is of class
\command{\link[=RMmodel-class]{RMmodel}}.\cr
The following models are available
(cf. \command{\link{RFgetModelNames}}):
%Choose from the following covariance models
\bold{Basic stationary and isotropic models}
\tabular{ll}{
\command{\link{RMcauchy}} \tab Cauchy family \cr
\command{\link{RMexp}} \tab exponential model \cr
\command{\link{RMgencauchy}} \tab generalized Cauchy family \cr
\command{\link{RMgauss}} \tab Gaussian model \cr
\command{\link{RMgneiting}} \tab differentiable model with compact support \cr
\command{\link{RMmatern}} \tab Whittle-Matern model \cr
\command{\link{RMnugget}} \tab nugget effect model \cr
\command{\link{RMspheric}} \tab spherical model \cr
\command{\link{RMstable}} \tab symmetric stable family or powered exponential model \cr
\command{\link{RMwhittle}} \tab Whittle-Matern model, alternative
parametrization\cr
}
\bold{Variogram models (stationary increments/intrinsically stationary)}
\tabular{ll}{
\command{\link{RMfbm}} \tab fractal Brownian motion\cr
}
\bold{Basic Operations}
\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{Basic models for mixed effect modelling}
% \tabular{ll}{
% \command{\link{RMfixcov}} \tab constant pre-defined covariance \cr
% \command{\link{RMfixed}} \tab fixed or trend effects;
% caution: \link{RMfixed} is not
% a function and can be used only in \link[=RFformula]{formula notation}.\cr
% %\command{\link{RMmixed}} \tab Mixture of fixed, mixed, and random effect
% %model\cr % gibts nur noch intern
% }
\bold{Others}
\tabular{ll}{
\command{\link{RMtrend}} \tab trend \cr
\command{\link{RMangle}} \tab defines a 2x2 anisotropy matrix by
rotation and stretch arguments.
}
% \bold{See \link{RMmodelsAdvanced} for many more, advanced models.\cr
% \bold{See \link{spherical models} for models valid on spherical
%coordinate systems.}
% }
}
\references{
\itemize{
\item Chiles, J.-P. and Delfiner, P. (1999)
\emph{Geostatistics. Modeling Spatial Uncertainty.}
New York: Wiley.
% \item Gneiting, T. and Schlather, M. (2004)
% Statistical modeling with covariance functions.
% \emph{In preparation.}
\item Schlather, M. (1999) \emph{An introduction to positive definite
functions and to unconditional simulation of random fields.}
Technical report ST 99-10, Dept. of Maths and Statistics,
Lancaster University.
\item Schlather, M. (2011) Construction of covariance functions and
unconditional simulation of random fields. In Porcu, E., Montero, J.M.
and Schlather, M., \emph{Space-Time Processes and Challenges Related
to Environmental Problems.} New York: Springer.
\item Yaglom, A.M. (1987) \emph{Correlation Theory of Stationary and
Related Random Functions I, Basic Results.}
New York: Springer.
\item Wackernagel, H. (2003) \emph{Multivariate Geostatistics.} Berlin:
Springer, 3nd edition.
}
}
\author{Alexander Malinowski; \martin}
\seealso{
\link{RM} for an overview over more advanced classes of models\cr
\link{RC}, \link{RF}, \link{RP}, \link{RR}, \link{R.},
\command{\link{RFcov}},
\command{\link{RFformula}},
\command{\link{RMmodelsAdvanced}},
\command{\link{RMmodelsAuxiliary}},
\link{trend modelling}
}
\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
## an example of a simple model
model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget
plot(model)
\dontshow{FinalizeExample()}}
|
