swh:1:snp:e520bf41b0e99213acde680a9d87fadac1aee079
Tip revision: f082dc8b0950aff830aab568d89a74af74f10e14 authored by Martin Schlather on 12 August 2014, 00:00:00 UTC
version 3.0.35
version 3.0.35
Tip revision: f082dc8
RMstp.Rd
\name{RMstp}
\alias{RMstp}
\alias{RMstp}
\title{Single temporal process}
\description{
\command{\link{RMstp}} is a univariate covariance model which depends on
a submodel \eqn{\phi}{phi} wich is a normal mixture model.
The covariance is given by
\deqn{
C(x,y) = |S_x|^{1/4} |S_y|^{1/4} |A|^{-1/2}
\phi(Q(x,y)^{1/2})
}
where
\deqn{
Q(x,y) = c^2 - m^2 + h^t (S_x + 2(m + c)M) A^{-1} (S_y + 2
(m-c)M)h,
}
\deqn{
c = -z^t h + \xi_2(x) - \xi_2(y),
}
\deqn{
A = S_x + S_y + 4 M h h^t M
}
\deqn{
m = h^t M h
}
\deqn{
h = x - y
}
}
\usage{
RMstp(xi, phi, S, z, M, var, scale, Aniso, proj)
}
\arguments{
\item{xi}{arbitrary univariate function on \eqn{R^d}}
\item{phi}{an \command{\link{RMmodel}} that is a normal mixture model}
\item{S}{functions that returns strictly positive definite
\eqn{d\times d}{d x d}}
\item{z}{arbitrary vector, \eqn{z \in R^d}}
\item{M}{an arbitrary, symmetric \eqn{d \times d}{d x d} matrix}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any \command{\link{RMmodel}}. If not passed, the above covariance function remains unmodified.}
}
\details{
See Schlather (2008) formula (13).
The model allows for mimicking cyclonic behaviour.
}
\value{
\command{\link{RMstp}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item Paciorek C.J., and Schervish, M.J. (2006)
Spatial modelling using a new class of nonstationary covariance functions,
\emph{Environmetrics} \bold{17}, 483-506.
\item Schlather, M. (2010)
Some covariance models based on normal scale mixtures.
\emph{Bernoulli}, \bold{16}, 780-797.
}
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\keyword{spatial}
\keyword{models}
\examples{
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMstp(xi = RMrotat(phi= -2 * pi, speed=1),
phi = RMwhittle(nu = 1),
M=matrix(nc=3, rep(0, 9)),
S=RMetaxxa(E=rep(1, 3), alpha = -2 * pi,
A=t(matrix(nc=3, c(2, 0, 0, 1, 1 , 0, 0, 0, 0))))
)
x <- seq(0, 10, if (interactive()) 0.7 else 5)
plot(RFsimulate(model, x=x, y=x, z=x))
\dontshow{FinalizeExample()}
}