https://github.com/cran/RandomFields
Tip revision: 0e562f038613e9388e8c33a6cf59f7f57ae62bf5 authored by Martin Schlather on 03 August 2014, 00:00:00 UTC
version 3.0.32
version 3.0.32
Tip revision: 0e562f0
RPschlather.Rd
\name{ExtremalGaussian}
\alias{RPschlather}
\alias{extremal Gaussian}
\alias{extremal Gaussian process}
\title{Extremal Gaussian process}
\description{
\command{RPschlather} defines an extremal Gaussian process.
}
\usage{
RPschlather(phi, tcf, xi, mu, s)
}
\arguments{
\item{phi}{an \command{\link{RMmodel}}, see Details.}
\item{tcf}{an \command{\link{RMmodel}} specifying the
extremal correlation function; either \code{phi} or \code{tcf} must
be given.}
\item{xi,mu,s}{the extreme value index, the location parameter and the
scale parameter, respectively, of the generalized extreme value
distribution. See 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.
The argument \code{phi} can be any random field for
which the expectation of the positive part is known at the origin.
It simulates Extremal Gaussian process \eqn{Z} (also
called \dQuote{Schlather model}), which is defined by
\deqn{Z(x) = \max_{i=1}^\infty X_i \max(0, Y_i(x)),
}{Z(x) = max_{i=1, 2, ...} X_i * max(0, Y_i(x)),}
where the \eqn{X_i} are the points of a Poisson point process on the
positive real half-axis with intensity \eqn{c x^{-2} dx}{c/x^2 dx},
\eqn{Y_i \sim Y}{Y_i ~ Y}
are iid stationary Gaussian processes with a covariance function
given by \code{model}, and \eqn{c} is chosen such
that \eqn{Z} has standard Frechet margins. \code{model} must
represent a stationary covariance model.
}
\note{Advanced options
are \code{maxpoints} and \code{max_gauss}, see
\command{\link{RFoptions}}.}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
\url{http://ms.math.uni-mannheim.de/de/publications/software}
}
\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
x <- seq(0, 2, if (interactive()) 0.01 else 1)
## standard use of RPschlather (i.e. a standardized Gaussian field)
z <- RFsimulate(RPschlather(RMgauss()), x)
plot(z, type="l")
## the following refers to the standard use, but obviously is incorrect
try(RFsimulate(model=RPschlather(RMgauss(var=2)), x=x, grid=TRUE))
## the following refers to the generalized use of RPschlather, where
## any random field can be used. Note that 'z' and 'z2' have the same
## .Random.seed (and the same simulation method), hence the same values
z2 <- RFsimulate(model=RPschlather(RPgauss(RMgauss(var=2))), x=x, grid=TRUE)
plot(z2, type="l")
all.equal(z, z2) # true
\dontshow{if (.C("isAuthor", a=integer(1))$a) { # OK
model <- RMgauss()
x <- seq(0,10, 0.02)
z <- RFsimulate(RPschlather(model, xi=0), x,
n=if (interactive()) 100 else 1)
plot(z)
hist(unlist(z@data), 50, freq=FALSE)
curve(exp(-x) * exp(-exp(-x)), from=-3, to=8, add=TRUE)
## for some more sophisticated models see 'maxstableAdvanced'
}}
\dontshow{FinalizeExample()}
}
\seealso{
\command{\link{RMmodel}},
\command{\link{RPgauss}},
\command{\link{maxstable}},
\command{\link{maxstableAdvanced}}
}
\keyword{spatial}