https://github.com/cran/RandomFields
Tip revision: 919f138ae97c73da2321579cf0a01351bf9ebff3 authored by Martin Schlather on 11 October 2016, 18:32:27 UTC
version 3.1.24.1
version 3.1.24.1
Tip revision: 919f138
RMstein.Rd
\name{RMstein}
\alias{RMstein}
\title{Stein nonseparable space-time model}
\description{
\command{\link{RMstein}} is a univariate stationary covariance model
whose corresponding covariance function only depends on the difference
\eqn{h}{h} between two points and is given by
\deqn{C(h, t) = W_{\nu}(y) - ( < h, z > t)/((\nu - 1)(2\nu + d))
* W_{\nu-1}(y)}{ C(h, t) = W_\nu(y) - < h, z > t W_{\nu-1}(y) / [
(\nu-1) (2\nu + d + 1) ]}
Here \eqn{W_\nu} is the covariance of the
\command{\link{RMwhittle}} model with
smoothness parameter \eqn{\nu};
\eqn{y=\|(h,t)\|}{y = ||(h,t)||} is the norm of the vector
\eqn{(h,t)}{(h,t)},
\eqn{d}{d} is the dimension of the space on which the random field is considered.
}
\usage{
RMstein(nu, z, var, scale, Aniso, proj)
}
\arguments{
\item{nu}{numerical value; greater than 1; smoothness parameter of the
RMwhittle model}
\item{z}{a vector; the norm of \eqn{z}{z} must be less or equal to 1.}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\details{See Stein (2005).
}
\value{
\command{\link{RMstein}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item Stein, M.L. (2005) Space-time covariance functions.
\emph{J. Amer. Statist. Assoc.} \bold{100}, 310-321. Equation (8).
}
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\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
\dontshow{StartExample()}
model <- RMstein(nu=1.5, z=0.9)
x <- seq(0, 10, 0.05)
plot(RFsimulate(model, x=x, y=x))
\dontshow{FinalizeExample()}
}