Revision 9298a5792ec3101f8d2a98edeb37d86b7263e34e authored by Martin Schlather on 24 July 2015, 00:00:00 UTC, committed by Gabor Csardi on 24 July 2015, 00:00:00 UTC
1 parent 84ac777
RMbr2.Rd
\name{RMbr2eg}
\alias{RMbr2eg}
\title{Transformation from Brown-Resnick to Gauss}
\description{
This function can be used to model a max-stable process
based on the a binary field, with the same extremal correlation
function as a Brown-Resnick process
\deqn{
C_{eg}(h) = 1 - 2 (1 - 2 \Phi(\sqrt{\gamma(h) / 2}) )^2
}
Here, \eqn{\Phi} is the standard normal distribution
function, and \eqn{\gamma} is a \bold{semi-}variogram with sill
\deqn{ 4(erf^{-1}(1/\sqrt 2))^2 = 2 * [\Phi^{-1}( [1 + 1/\sqrt 2] /
2)]^2 = 4.425098 / 2 = 2.212549}
}
\usage{
RMbr2eg(phi, var, scale, Aniso, proj)
}
\arguments{
\item{phi}{covariance function of class \code{\link[=RMmodel-class]{RMmodel}}.}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\value{
object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\details{
\command{\link{RMbr2eg}} \cr
The extremal Gaussian model \command{\link{RPschlather}}
simulated with \code{\link{RMbr2eg}(\link{RMmodel}())} has
tail correlation function that equals
the tail correlation function of Brown-Resnick process with
variogram \command{\link{RMmodel}}.
Note that the reference paper is based on the notion of the
(genuine) variogram, whereas the package \pkg{RandomFields}
is based on the notion of semi-variogram. So formulae
differ by factor 2.
}
\references{
\itemize{
\item Strokorb, K., Ballani, F., and Schlather, M. (2014)
Tail correlation functions of max-stable processes: Construction
principles, recovery and diversity of some mixing max-stable processes
with identical TCF.
\emph{Extremes}, \bold{} Submitted.
}
}
\seealso{
\link{maxstableAdvanced},
\command{\link{RMbr2bg}},
\command{\link{RMmodel}},
\command{\link{RMm2r}},
\command{\link{RPbernoulli}},
\command{\link{RPbrownresnick}},
\command{\link{RPschlather}},
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
\url{http://ms.math.uni-mannheim.de/de/publications/software}
}
\keyword{spatial}
\examples{
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
\dontshow{StartExample(reduced=20)}
model <- RMexp(var=1.62 / 2)
binary.model <- RPbernoulli(RMbr2bg(model))
x <- seq(0, 10, 0.05)
z <- RFsimulate(RPschlather(binary.model), x, x)
plot(z)
\dontshow{FinalizeExample()}
}
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