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
RMbcw.Rd
\name{RMbcw}
\alias{RMbcw}
\title{Model bridging stationary and intrinsically stationary processes}
\description{
\command{\link{RMbcw}} is a variogram model
that bridges between some intrinsically stationary isotropic processes
and some stationary ones. It reunifies the
\command{\link{RMgenfbm}} \sQuote{b}, \command{\link{RMgencauchy}} \sQuote{c}
and \command{\link{RMdewijsian}} \sQuote{w}.
The corresponding centered semi-variogram only depends on the distance
\eqn{r \ge 0}{r \ge 0} between two points and is given by
\deqn{\gamma(r) =
\frac{(r^{\alpha}+1)^{\beta/\alpha}-1}{2^{\beta/\alpha} -1}}{
\gamma(r)=[(r^{\alpha}+1)^{\beta/\alpha}-1] / (2^{\beta/\alpha}-1)}
where \eqn{\alpha \in (0,2]}{0 < \alpha \le 2} and \eqn{\beta \le 2}{\beta <= 2}.\cr
}
\usage{
RMbcw(alpha, beta, c, var, scale, Aniso, proj)
}
\arguments{
\item{alpha}{a numerical value; should be in the interval (0,2].}
\item{beta}{a numerical value; should be in the interval (-infty,2].}
\item{c}{only for experts. If given, a not necessarily positive definite
function \eqn{c-\gamma(r)} is built.}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
variogram remains unmodified.}
}
\details{
For \eqn{\beta >0}, \eqn{\beta<0}, \eqn{\beta=0}
we have the generalized fractal Brownian motion \command{\link{RMgenfbm}},
the generalized Cauchy model \command{\link{RMgencauchy}},
and the de Wisjian model \command{\link{RMdewijsian}}, respectively.
Hence its two arguments \code{alpha} and \code{beta}
allow for modelling the smoothness and a wide range of tail behaviour,
respectively.
}
\value{
\command{\link{RMbcw}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item Schlather, M (2014) A parametric variogram model bridging
between stationary and intrinsically stationary processes. \emph{arxiv}
\bold{1412.1914}.
% \item Martin's Toledo-Chapter: Construction of covariance functions
% and unconditional simulation of random fields, Application to variograms
}
}
\me
\seealso{
\command{\link{RMlsfbm}} is equipped with Matheron's constant \eqn{c} for
the fractional brownian motion,
\command{\link{RMgenfbm}},
\command{\link{RMgencauchy}},
\command{\link{RMdewijsian}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\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
model <- RMbcw(alpha=1, beta=0.5)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}}