\name{RMbr2bg}
\alias{RMbr2bg}
\title{Transformation from Brown-Resnick to Bernoulli}
\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_{bg}(h) = \cos(\pi (2\Phi(\sqrt{\gamma(h) / 2}) -1) )
}
Here, \eqn{\Phi} is the standard normal distribution
function, and \eqn{\gamma} is a \bold{semi-}variogram with sill
\deqn{4(erf^{-1}(1/2))^2 = 2 * { \Phi^{-1}( 3 / 4 ) }^2 =
1.819746 / 2 = 0.9098728}
}
\usage{
RMbr2bg(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{RMbr2bg}} \cr
binary random field \command{\link{RPbernoulli}}
simulated with \code{\link{RMbr2bg}(\link{RMmodel}())} has
a uncentered covariance function that equals
\enumerate{
\item
the tail correlation function of
the max-stable process constructed with this binary random field
\item
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{RMbr2eg}},
\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
model <- RMexp(var=1.62 / 2)
step <- if (interactive()) 0.05 else 2
y <- seq(0, 10, step)
z <- RFsimulate(RPschlather(RMbr2eg(model)), y, y)
plot(z)
\dontshow{FinalizeExample()}
}