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\name{Brown-Resnick-Specific}
\alias{BRmethods}
\alias{RPbrmixed}
\alias{RPbrorig}
\alias{RPbrshifted}
\alias{RPloggaussnormed}
\title{Simulation methods for Brown-Resnick processes}
\description{
These models define particular ways to simulate Brown-Resnick
processes.
}
\usage{
RPbrmixed(phi, tcf, xi, mu, s, meshsize, vertnumber, optim_mixed,
optim_mixed_tol,lambda, areamat, variobound)
RPbrorig(phi, tcf, xi, mu, s)
RPbrshifted(phi, tcf, xi, mu, s)
RPloggaussnormed(variogram, prob, optimize_p, nth, burn.in, rejection)
}
\arguments{
\item{phi,variogram}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the covariance model to be simulated.}
\item{tcf}{the extremal correlation function; either \code{phi} or
\code{tcf} must be given.}
\item{xi, mu, s}{the shape parameter, the location parameter and the
scale parameter, respectively, of the generalized extreme value
distribution. See Details.}
\item{lambda}{positive constant factor in the intensity of the Poisson
point process used in the M3 representation, cf. Thm. 6 and Remark 7
in Oesting et. al (2012); can be estimated by setting
\code{optim_mixed} if unknown. Default value is 1.}
\item{areamat}{vector of values in \eqn{[0,1]}. The value of the \eqn{k}{k}th
component represents the portion of processes whose maximum is located at a
distance \eqn{d} with \eqn{k-1 \leq d < k}{k-1 <= d < k} from the origin
taken into account for the simulation of the shape function in the M3
representation. \code{areamat} can be used for isotropic models only; can be
optimized by setting \code{optim_mixed} if unknown. Default value is 1.}
\item{meshsize, vertnumber, optim_mixed,
optim_mixed_tol, variobound}{further arguments
for simulation via the mixed moving maxima (M3) representation; see
\code{\link{RFoptions}}.}
\item{prob}{to do
}
\item{optimize_p}{to do
}
\item{nth}{to do
}
\item{burn.in}{to do
}
\item{rejection}{to do
}
}
\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 values or given an \code{\link{RMmodel}}, in particular by an
\code{\link{RMtrend}} model.
The functions \code{RPbrorig}, \code{RPbrshifted} and \code{RPbrmixed}
simulate a Brown-Resnick process, which is defined by
\deqn{Z(x) = \max_{i=1}^\infty X_i \exp(W_i(x) - \gamma),
}{Z(x) = max_{i=1, 2, ...} X_i * exp(W_i(x) - gamma),}
where the \eqn{X_i} are the points of a Poisson point process on the
positive real half-axis with intensity \eqn{x^{-2} dx}{1/x^2 dx},
\eqn{W_i \sim W}{W_i ~ Y} are iid centered Gaussian processes with
stationary increments and variogram \eqn{\gamma}{gamma} given by
\code{model}. The functions correspond to the following ways of
simulation:
\describe{
\item{\code{RPbrorig}}{simulation using the original definition
(method 0 in Oesting et al., 2012)}
\item{\code{RPbrshifted}}{simulation using a random shift (similar to
method 1 and 2)}
\item{\code{RPbrmixed}}{simulation using M3 representation (method
4)}
}
}
\value{
The functions return an object of class
\code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Oesting, M., Kabluchko, Z. and Schlather M. (2012)
Simulation of {B}rown-{R}esnick Processes, \emph{Extremes},
\bold{15}, 89-107.
}}
\note{Advanced options for \code{RPbroriginal} and \code{RPbrshifted}
are \code{maxpoints} and \code{max_gauss}, see \command{\link{RFoptions}}.}
\author{\marco; \martin}
\examples{\dontshow{StartExample()}
#
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
% TO DO
## currently does not work
\dontshow{\dontrun{
model <- RPbrshifted(RMfbm(alpha=1.5), xi=0)
x <- 0:10
z <- RFsimulate(model=model, x=x, y=x, n=4)
plot(z)
}}
\dontshow{FinalizeExample()}
}
\seealso{
\command{\link{RPbrownresnick}},
\command{\link{RMmodel}},
\command{\link{RPgauss}},
\command{\link{maxstable}},
\command{\link{maxstableAdvanced}}.
}
\keyword{methods}
|
