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.}
\item{model}{string; see \code{\link{CovarianceFct}}, or
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,
see \code{\link{RFMethods}}, or
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
\code{\link{GaussRF}}.
\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,
see \code{\link{RFMethods}}. Hence, only
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
\code{MaxStableRF} and \code{\link{DoSimulateRF}} return \code{NULL}
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{
\code{\link{CovarianceFct}},
\code{\link{GaussRF}},
\code{\link{RandomFields}},
\code{\link{RFMethods}},
\code{\link{RFparameters}},
\code{\link{DoSimulateRF}},
.
}
\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 ...
```

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