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\name{RMgenfbm}
\alias{RMgenfbm}
\title{Generalized Fractal Brownian Motion Variogram Model}
\description{
\command{\link{RMgenfbm}} 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) = (r^{\alpha}+1)^{\beta/\alpha}-1}{\gamma(r)=(r^{\alpha}+1)^{\beta/\alpha}-1}
where \eqn{\alpha \in (0,2]}{0 < \alpha \le 2} and \eqn{\beta \in (0,2]}.\cr
See also \command{\link{RMfbm}}.
}
\usage{
RMgenfbm(alpha, beta, var, scale, Aniso, proj)
}
\arguments{
\item{alpha}{a numerical value; should be in the interval (0,2].}
\item{beta}{a numerical value; should be in the interval (0,2].}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
variogram remains unmodified.}
}
\details{
Here, the variogram of \command{\link{RMfbm}} is modified by
the transformation \eqn{(\gamma+1)^{\delta/-1}} on variograms
\eqn{\gamma}
for \eqn{\delta \in (0,1]}. This original modification allows for
further generalization, cf. \command{\link{RMbcw}}.
}
\value{
\command{\link{RMgenfbm}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Gneiting, T. (2002) Nonseparable, stationary covariance
functions for space-time data, \emph{JASA} \bold{97}, 590-600.
\item
Schlather, M. (2010)
On some covariance models based on normal scale mixtures.
\emph{Bernoulli}, \bold{16}, 780-797.
% \item Martin's Toledo-Chapter: Construction of covariance functions
% and unconditional simulation of random fields, Application to variograms
}
}
\me
\seealso{
\command{\link{RMbcw}},
\command{\link{RMfbm}},
\command{\link{RMmodel}},
\command{\link{RMflatpower}},
\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
model <- RMgenfbm(alpha=1, beta=0.5)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}}
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