https://github.com/cran/RandomFields
Tip revision: fd4911aa390fd49ddab92bd139bbbf35422e32e5 authored by Martin Schlather on 06 February 2020, 05:20:37 UTC
version 3.3.8
version 3.3.8
Tip revision: fd4911a
RMfractgauss.Rd
\name{RMfractgauss}
\alias{RMfractgauss}
\title{Fractal Gaussian Model Family}
\description{
\command{\link{RMfractgauss}} is a stationary isotropic covariance model.
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) = 0.5 ((r+1)^{\alpha}-2r^{\alpha}+|r-1|^{\alpha})}{C(r) = 0.5 ((r+1)^(\alpha)-2r^(\alpha)+|r-1|^(\alpha))}
with \eqn{0 < \alpha \le 2}. It can only be used for one-dimensional random fields.
}
\usage{
RMfractgauss(alpha,var, scale, Aniso, proj)
}
\arguments{
\item{alpha}{ \eqn{0 < \alpha \le 2}}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\details{The model is only valid for dimension \eqn{d = 1}{d = 1 }. It
is the covariance function for the fractional Gaussian noise with
self-affinity index (Hurst parameter) \eqn{H=\alpha /2}{H=\alpha /2} with \eqn{0 < \alpha \le 2}{0 < \alpha \le 2}.
}
\value{
\command{\link{RMfractgauss}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Gneiting, T. and Schlather, M. (2004)
Stochastic models which separate fractal dimension and Hurst effect.
\emph{SIAM review} \bold{46}, 269--282.
}
}
\me
\seealso{
\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
model <- RMfractgauss(alpha=0.5, scale=0.2)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}}