\name{Extremal t}
\alias{RPopitz}
\alias{extremal t}
\alias{extremal t process}

\title{Extremal t process}
\description{ 
  \command{RPopitz} defines an extremal t process.
}

\usage{
RPopitz(phi, xi, mu, s, alpha)
}

\arguments{
  \item{phi}{an \command{\link{RMmodel}};
    covariance model for a standardized
    Gaussian random fields, or the field itself.
  }
  \item{xi,mu,s}{the extreme value index, the location parameter and the
    scale parameter, respectively, of the generalized extreme value
    distribution. See Details.
  }
  \item{alpha}{originally referred to the \eqn{\alpha}-Frechet marginal
    distribution, see the original literature for details.
  }
}

\details{
  The argument \code{xi} is always a number, i.e. \eqn{\xi} is constant in
  space. In contrast, \eqn{\mu} and \eqn{s} might be constant
 numerical value or given a \code{\link{RMmodel}}, in particular by a
 \code{\link{RMtrend}} model.  The default values of \eqn{mu} and \eqn{s}
 are \eqn{1} and \eqn{z\xi}, respectively.
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
 \url{http://ms.math.uni-mannheim.de/de/publications/software}
}

\references{
  \itemize{
    \item
    Davison, A.C., Padoan, S., Ribatet, M. (2012).
    Statistical modelling of spatial extremes.
    \emph{Stat. Science} \bold{27}, 161-186.
   \item
   Opitz, T. (2012) A spectral construction of the extremal t process.
    \emph{arxiv} \bold{1207.2296}.
  }
}

\seealso{
 \command{\link{RMmodel}},
 \command{\link{RPgauss}},
 \command{\link{maxstable}},
 \command{\link{maxstableAdvanced}}
}

\keyword{spatial}


\examples{
RFoptions(seed=0, xi=0)
## seed=0: *ANY* simulation will have the random seed 0; set
##         RFoptions(seed=NA) to make them all random again
## xi=0: any simulated max-staable random field has extreme value index 0
\dontshow{StartExample()}
x <- seq(0, 2, 0.01)
model <- RPopitz(RMgauss(), alpha=2)
z1 <- RFsimulate(model, x)
plot(z1, type="l")

\dontshow{FinalizeExample()}
}