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, or 5 (see the argument \code{orig}).
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 \le r \le \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(orig, 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.}
\item{orig}{logical.
If \code{TRUE} the above model is used.
Otherwise
the \code{\link{RMgengneiting}} model C(s r) with \code{kappa=3} as above, but with \code{mu = 2.683509} and \code{s=0.2745640815} is used.
The latter has the advantage of being closer to the Gaussian model and
it is valid up to dimension 5.
Default: \code{TRUE}.
}
}
\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 for \eqn{\mu=1.5}: \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{
For the original version
\itemize{
\item Gneiting, T. (1999)
Correlation functions for atmospherical data analysis.
\emph{Q. J. Roy. Meteor. Soc} Part A \bold{125}, 2449-2464.
}
For the version (\code{orig=FALSE})
\itemize{
\item this package \pkg{RandomFields}.
}
}
\me
\seealso{
\command{\link{RMbigneiting}},
\command{\link{RMgengneiting}},
\command{\link{RMgauss}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\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
plot(RMgneiting(), model2=RMgneiting(orig=FALSE), model3=RMgauss(),
xlim=c(-3,3), maxchar=100)
plot(RMgneiting(), model2=RMgneiting(orig=FALSE), model3=RMgauss(),
xlim=c(1.5,2.5), maxchar=100)
model <- RMgneiting(orig=FALSE, scale=0.4)
x <- seq(0, 10, 0.2) ## nicer with 0.1 instead of 0.2
z <- RFsimulate(model, x=x, y=x, z=x, T=c(1,1,4), maxGB=3)
plot(z, MARGIN.slices=4, MARGIN.movie=3)
\dontshow{FinalizeExample()}}