https://github.com/cran/RandomFields
Tip revision: e994a4415e67fa60cbfd3f208aaab20872521c0b authored by Martin Schlather on 14 February 2019, 21:02:19 UTC
version 3.3
version 3.3
Tip revision: e994a44
RPcoin.Rd
\name{Coins}
\alias{Coins}
\alias{RPcoins}
\alias{Average}
\alias{RPaverage}
\title{Random coin method}
\description{
The random coin method (or dilution method) is a simulation method for
stationary Gaussian random fields. It is based on the following procedure:
For a stationary Poisson point process on \eqn{{\bf R}^d}{R^d}
consider the random field
\deqn{Y(y) = \sum_{x\in X} f(y-x)}{Y(y) = \sum_{x\in X} f(y-x)}
for a function \eqn{f}{f}. The covariance of \eqn{Y}{Y} is
proportional to the convolution
\deqn{C(h) = \int f(x)f(x+h) dx }{C(h) = \int f(x)f(x+h) dx}
If the intensity of the Poisson point process increases, the
random field \eqn{Y}{Y} approaches a Gaussian random field
with covariance function \eqn{C}{C}.
}
\usage{
RPcoins(phi, shape, boxcox, intensity, method)
RPaverage(phi, shape, boxcox, intensity, method)
}
\arguments{
\item{phi}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the covariance function of the Poisson process;
either \code{phi} or \code{shape} must be given.
}
\item{shape}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the function which is attached to the Poisson points;
note that this is not the covariance function of the simulated
random field.}
\item{boxcox}{the one or two parameters of the box cox transformation.
If not given, the globally defined parameters are used.
See \command{\link{RFboxcox}} for details.
}
\item{intensity}{positive number, intensity of the underlying Poisson
point process.
}
\item{method}{integer.
Default is the value \code{0} which addresses the current standard
procedure. There might be further methods implemented mainly for
internal purposes.
}
}
%\details{}
\value{
\command{\link{RPcoins}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Lantuejoul, C. (2002)
\emph{Geostatistical Simulation: Models and Algorithms.}
Springer.
}}
\me
\seealso{ \link{Gaussian},
\link{RP},
\command{\link{RPhyperplane}},
\command{\link{RPspectral}},
\command{\link{RPtbm}}.
}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
\dontshow{\dontrun{
x <- seq(0,25, 0.02)
model <- RPcoins(RMspheric())
z <- RFsimulate(model, x, x, spConform=FALSE) # takes 20 sec
Print(sd(as.vector(z)), mean(z))
image(z)
### Gaussian field approximated by Poisson fields
x <- seq(0,10, 0.02)
for (intensity in c(1, 10, 100)) {
z <- RFsimulate(x=x, model=RPcoins(RMspheric(), intensity = intensity))
plot(z)
}
}}
\dontshow{FinalizeExample()}}
\keyword{methods}