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
RMtbm.Rd
\name{RMtbm}
\alias{RMtbm}
\title{Turning Bands Method}
\description{
\command{\link{RMtbm}} is a univariate or multivaraiate stationary isotropic covariance
model in dimension \code{reduceddim} which depends on a univariate or
multivariate stationary
isotropic covariance \eqn{\phi}{phi} in a bigger dimension \code{fulldim}.
For formulas for the covariance function see details.
}
\usage{
RMtbm(phi, fulldim, reduceddim, layers, var, scale, Aniso, proj)
}
\arguments{
\item{phi, fulldim, reduceddim, layers}{See \command{\link{RPtbm}}.}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\value{
\command{\link{RMtbm}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\details{
The turning bands method stems from the 1:1 correspondence between the
isotropic covariance functions of different dimensions. See Gneiting
(1999) and Strokorb and Schlather (2014).
The standard case is \code{reduceddim=1} and \code{fulldim=3}.
If only one of the arguments is given, then the difference of the two
arguments equals 2.
For \code{d == n + 2}, where \code{n=reduceddim} and
\code{d==fulldim} the original dimension, we have
\deqn{
C(r) = \phi(r) + r \phi'(r) / n
}{
C(r) = phi(r) + r phi'(r) / n
}
which for \code{n=1} reduces to the standard TBM operator
\deqn{
C(r) =\frac {d}{d r} r \phi(r)
}{
C(r) = d/dr [ r phi(r) ]
}
For \code{d == 2 && n == 1} we have
\deqn{
C(r) = \frac{d}{dr}\int_0^r \frac{u\phi(u)}{\sqrt{r^2 - u^2}} d u
}{
C(r) = d/dr int_0^r [ r phi(r) ] / [ sqrt{r^2 - u^2} ] d u
}
\sQuote{Turning layers} is a generalization of the turning bands
method, see Schlather (2011).
}
\references{
Turning bands
\itemize{
\item Gneiting, T. (1999)
On the derivatives of radial positive definite function.
\emph{J. Math. Anal. Appl}, \bold{236}, 86-99
\item
Matheron, G. (1973).
The intrinsic random functions and their applications.
\emph{Adv . Appl. Probab.}, \bold{5}, 439-468.
\item
Strokorb, K., Ballani, F., and Schlather, M. (2014)
Tail correlation functions of max-stable processes: Construction
principles, recovery and diversity of some mixing max-stable
processes with identical TCF.
\emph{Extremes}, \bold{} Submitted.
}
Turning layers
\itemize{
\item Schlather, M. (2011) Construction of covariance functions and
unconditional simulation of random fields. In Porcu, E., Montero, J.M.
and Schlather, M., \emph{Space-Time Processes and Challenges Related
to Environmental Problems.} New York: Springer.
}
}
\seealso{
\command{\link{RPtbm}},
\command{\link{RFsimulate}}.
}
\me
\keyword{spatial}
\keyword{models}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
x <- seq(0, 10, 0.02)
model <- RMspheric()
plot(model, model.on.the.line=RMtbm(RMspheric()), xlim=c(-1.5, 1.5))
z <- RFsimulate(RPtbm(model), x, x)
plot(z)
\dontshow{FinalizeExample()}}