\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

model <- RMexp(var=1.62 / 2) 
binary.model <- RPbernoulli(RMbr2bg(model))
step <- if (interactive()) 0.05 else 2
y <- seq(0, 10, step)
z <- RFsimulate(RPschlather(binary.model), y, y)
plot(z)

\dontshow{FinalizeExample()}
}