https://github.com/cran/RandomFields
Tip revision: 51663e75fb9ba1d6cf08d8f47db96cebfe1bb458 authored by Martin Schlather on 04 December 2013, 00:00:00 UTC
version 3.0.5
version 3.0.5
Tip revision: 51663e7
RMdewijsian.Rd
\name{RMdewijsian}
\alias{RMdewijsian}
\title{Generalized DeWijsian Variogram Model}
\description{
\command{\link{RMdewijsian}} is an intrinsically stationary isotropic variogram model.
The corresponding centered semi-variogram only depends on the distance
\eqn{r \ge 0}{r \ge 0} between two points and is given by
\deqn{\gamma(r) = \log(r^{\alpha}+1)}{\gamma(r)=log(r^{\alpha}+1)}
where \eqn{\alpha \in (0,2]}{0 < \alpha \le 2}.
}
\usage{
RMdewijsian(alpha, var, scale, Aniso, proj)
}
\arguments{
\item{alpha}{a numerical value; should be in the interval (0,2]
to provide a valid variogram for a random field of any dimension.}
\item{var,scale,Aniso,proj}{optional parameters; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
variogram remains unmodified.}
}
\details{
The parameter \eqn{\alpha}{\alpha} must satisfy \eqn{\alpha \in (0,2]}{0
< \alpha \le 2}.
Originally, the logarithmic model \eqn{\gamma(r) = \log(r)} was named
after de Wijs and reflects a principle of similarity (cf. Chiles,
J.-P. and Delfiner, P. (1999), p. 90).
But note that \eqn{\gamma(r) = \log(r)} is not a valid variogram
(\eqn{\gamma(0)} does not vanish)
whereas \eqn{\gamma(r) = \log(r^{\alpha}+1)} is valid
(cf. Wackernagel, H. (2003), p. 336).
}
\value{
\command{\link{RMdewijsian}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item Chiles, J.-P. and Delfiner, P. (1999)
\emph{Geostatistics. Modeling Spatial Uncertainty.}
New York: Wiley.
\item Wackernagel, H. (2003) \emph{Multivariate Geostatistics.} Berlin:
Springer, 3nd edition.
% \item Martin's Toledo-Chapter: Construction of covariance functions
% and unconditional simulation of random fields, Example 7
}
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\keyword{spatial}
\keyword{models}
\examples{
set.seed(0)
model <- RMdewijsian(alpha=1)
x <- seq(0, 10, if (interactive()) 0.02 else 1)
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
}