https://github.com/cran/RandomFields
Tip revision: f082dc8b0950aff830aab568d89a74af74f10e14 authored by Martin Schlather on 12 August 2014, 00:00:00 UTC
version 3.0.35
version 3.0.35
Tip revision: f082dc8
RMgauss.Rd
\name{RMgauss}
\alias{RMgauss}
\title{Gaussian Covariance Model}
\description{
\command{\link{RMgauss}} is a stationary isotropic covariance model.
The corresponding covariance function only depends on the distance
\eqn{r \ge 0}{r \ge 0} between two points and is given by
\deqn{C(r) = e^{-r^2}}{C(r)=e^{-r^2}.}
}
\usage{
RMgauss(var, scale, Aniso, proj)
}
\arguments{
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\details{
This model is called Gaussian because of the functional similarity of
the spectral density of a process with that covariance function to the
Gaussian probability density function.
The Gaussian model has an infinitely differentiable covariance
function. This smoothness is artificial. Furthermore, this often leads to
singular matrices and therefore numerically instable procedures
(cf. Stein, M. L. (1999), p. 29).
% See \command{\link{RMgneiting}} for an alternative model that does not
% have the disadvantages of the Gaussian model.
The Gaussian model is included in the symmetric stable class (see
\command{\link{RMstable}}) for the choice \eqn{\alpha = 2}{alpha = 2}.
}
\value{
\command{\link{RMgauss}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp,
P. (eds.) (2010) \emph{Handbook of Spatial Statistics.}
Boca Raton: Chapman & Hall/CRL.
Stein, M. L. (1999) \emph{Interpolation of Spatial Data.} New York: Springer-Verlag
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\command{\link{RMstable}} and \command{\link{RMmatern}} for generalisations;
\cr
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
Do not mix up with \command{\link{RPgauss}} or \command{\link{RRgauss}}.
}
\keyword{spatial}
\keyword{models}
\examples{
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMgauss(scale=0.4)
x <- seq(0, 10, if (interactive()) 0.02 else 1)
plot(model)
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}
}