https://github.com/cran/RandomFields
Tip revision: 0e562f038613e9388e8c33a6cf59f7f57ae62bf5 authored by Martin Schlather on 03 August 2014, 00:00:00 UTC
version 3.0.32
version 3.0.32
Tip revision: 0e562f0
RMgneiting.Rd
\name{RMgneiting}
\alias{RMgneiting}
\title{Gneiting Covariance Model}
\description{
\command{\link{RMgneiting}} is a stationary isotropic covariance model
which is only valid up to dimension 3.
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) = (1 + 8 s r + 25 s^2 r^2 + 32 s^3 r^3)(1-s r)^8 }{C(r) = (1 + 8 s r + 25 s^2 r^2 + 32 s^3 r^3)(1-s r)^8 }
if \eqn{0 \ge r \ge \frac{1}{s}}{0 <= r <= 1/s} and
\deqn{C(r)=0}{C(r)=0} otherwise. Here,
\eqn{s=0.301187465825}{s=0.301187465825}.
For a generalized model see also \command{\link{RMgengneiting}}.
}
\usage{
RMgneiting(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 isotropic covariance function is valid only for dimensions less than or equal to 3.
It is 6 times differentiable and has compact support.
This model is an alternative to \command{\link{RMgauss}} as its graph is hardly distinguishable from the
graph of the Gaussian model, but possesses neither the mathematical nor the numerical disadvantages of the Gaussian model.
It is a special case of \command{\link{RMgengneiting}} for the choice \eqn{kappa=3, \mu=1.5}{kappa=3, mu=1.5}.
Note that, in the original work by Gneiting (1999), a numerical value slightly deviating from
the optimal one was used: \eqn{s=\frac{10 \sqrt(2)}{47}}{s=10 sqrt(2)/47}.
}
\value{
\command{\link{RMgneiting}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Gneiting, T. (1999)
Correlation functions for atmospherical data analysis.
\emph{Q. J. Roy. Meteor. Soc} Part A \bold{125}, 2449-2464.
}
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\command{\link{RMbigneiting}},
\command{\link{RMgengneiting}},
\command{\link{RMgauss}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\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
scale <- 0.4
model <- RMgneiting(scale = scale)
x <- seq(0, 10, if (interactive()) 0.02 else 1)
plot(model, ylim=c(0,1))
points(x, RFcov(RMgauss(scale = scale), x), col="red")
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}
}