Revision da8174e204c4b3c8aff0fa179a0b53656129ef8e authored by Martin Schlather on 01 March 2004, 00:00:00 UTC, committed by Gabor Csardi on 01 March 2004, 00:00:00 UTC
1 parent 3e1677b
MaxStableRF.Rd
\name{MaxStableRF}
\alias{MaxStableRF}
\alias{InitMaxStableRF}
\title{Max-Stable Random Fields}
\description{
These functions simulate stationary and isotropic max-stable
random fields with unit Frechet margins.
}
\usage{
MaxStableRF(x, y=NULL, z=NULL, grid, model, param, maxstable,
method=NULL, n=1, register=0, gridtriple=FALSE)

InitMaxStableRF(x, y=NULL, z=NULL, grid, model, param, maxstable,
method=NULL, register=0, gridtriple=FALSE)
}
%- maybe also usage' for other objects documented here.
\arguments{
\item{x}{matrix of coordinates, or vector of x coordinates}
\item{y}{vector of y coordinates}
\item{z}{vector of z coordinates}
\item{grid}{logical; determines whether the vectors \code{x},
\code{y}, and \code{z} should be
interpreted as a grid definition, see Details.}
type \code{\link{PrintModelList}()} to get all options;
interpretation depends on the value of \code{maxstable},
see Details.}
\item{param}{parameter vector:
\code{param=c(mean, variance, nugget, scale,...)};
the parameters must be given
in this order; further parameters are to be added in case of a
parametrised class of covariance functions,
see \code{\link{CovarianceFct}}, or be given in one of the extended
forms, see Details}
\item{maxstable}{string. Either 'extremalGauss' or
'BooleanFunction'; see Details.}
\item{method}{\code{NULL} or string; method used for simulating,
type \code{\link{PrintMethodList}()} to get all options;
interpretation depends on the value of \code{maxstable}.}
\item{n}{number of realisations to generate}
\item{register}{0:9; place where intermediate calculations are stored;
the numbers are aliases for 10 internal registers}
\item{gridtriple}{logical;  if \code{gridtriple==FALSE} ascending
sequences for the parameters
\code{x}, \code{y}, and \code{z} are
expected; if \code{gridtriple==TRUE} triples of form
\code{c(start,end,step)}
expected; this parameter is used only
if \code{grid==TRUE}}
}
\details{
There are two different kinds of models for max-stable processes
implemented:
\itemize{
\item \code{maxstable="extremalGauss"}\cr
Gaussian random fields are multiplied by independent
random factors,
and the maximum is taken. The random factors are such that
the resulting random field has unit
Frechet margins; the specification of the random factor
is uniquely given by the specification of the random
field. The parameter vector \code{param}, the \code{model},
and the \code{method} are interpreted
in the same way as for Gaussian random fields, see

\item \code{maxstable="BooleanFunction"}\cr
Deterministic or random, upper semi-continuous
\eqn{L_1}{L1}-functions are randomly centred and multiplied by
suitable, independent random factors; the pointwise maximum over all
these functions yields a max-stable random field.
The simulation technique is related to the random coin
method for Gaussian random field simulation,
models that are suitable for the random coin method
are suitable for this technique, see \code{\link{PrintModelList}()}
for a complete list of suitable covariance models.\cr
The only value allowed for \code{method} is 'max.MPP' (and
\code{NULL}),
see \code{\link{PrintMethodList}()}. In the parameter list
\code{param} the first two entries, namely \code{mean} and
\code{variance}, are ignored. If the nugget is positive,
for each point an additional independent unit Frechet variable
with scale parameter
\code{nugget} is involved when building the maximum
over all functions.

The model may be defined alternatively in one of the two extended
ways as introduced in \code{CovarianceFct} and \code{GaussRF}.
However only a single model may be given! The model may be
anisotropic.
}
} \value{
\code{InitMaxStableRF} returns 0 if no error has occurred, and
a positive value if failed.\cr

if an error has occurred; otherwise the returned object
depends on the parameters:\cr
\code{n==1}:\cr
* \code{grid==FALSE}.  A vector of simulated values is
returned (independent of the dimension of the random field)\cr
* \code{grid==TRUE}.  An array of the dimension of the
random field is returned.\cr

\code{n>1}:\cr
* \code{grid==FALSE}.  A matrix is returned.  The columns
contain the repetitions.\cr
* \code{grid==TRUE}.  An array of dimension
\eqn{d+1}{d+1}, where \eqn{d}{d} is the dimension of
the random field, is returned.  The last
dimension contains the repetitions.

}
\references{
Schlather, M. (2002) Models for stationary max-stable
random fields. \emph{Extremes} \bold{5}, 33-44.
}
\author{Martin Schlather, \email{martin.schlather@cu.lu}
\url{http://www.cu.lu/~schlathe}}
\seealso{
.
}
\examples{
n <- 100
x <- y <- 1:n
ms <- MaxStableRF(x, y, grid=TRUE, model="exponen",
param=c(0,1,0,40), maxstable="extr")
image(x,y,ms)
}
\keyword{spatial}%-- one or more ...
` Computing file changes ...