https://github.com/cran/RandomFields
Tip revision: fd4911aa390fd49ddab92bd139bbbf35422e32e5 authored by Martin Schlather on 06 February 2020, 05:20:37 UTC
version 3.3.8
version 3.3.8
Tip revision: fd4911a
RFpseudomadogram.Rd
\name{RFpseudomadogram}
\alias{RFpseudomadogram}
\title{Empirical Pseudomadogram}
\description{
Calculates the empirical pseudomadogram. The empirical
pseudomadogram of two random fields \eqn{X}{X} and \eqn{Y}{Y} is given by
\deqn{\gamma(r):=\frac{1}{N(r)} \sum_{(t_{i},t_{j})|t_{i,j}=r} |(X(t_{i})-X(t_{j}))||(Y(t_{i})-Y(t_{j}))|}{\gamma(r):=1/N(r) \sum_{(t_{i},t_{j})|t_{i,j}=r} |(X(t_{i})-X(t_{j}))||(Y(t_{i})-Y(t_{j}))|}
where \eqn{t_{i,j}:=t_{i}-t_{j}}{t_{i,j}:=t_{i}-t_{j}}, and where \eqn{N(r)}{N(r)} denotes the number of pairs of data points with distancevector
\eqn{t_{i,j}=r}{t_{i,j}=r}.
}
\usage{
RFpseudomadogram(model, x, y=NULL, z=NULL, T=NULL, grid, params, distances,
dim, ..., data, bin=NULL, phi=NULL, theta = NULL,
deltaT = NULL, vdim=NULL)
}
\arguments{
\item{model,params}{\argModel }
\item{x}{\argX}
\item{y,z}{\argYz}
\item{T}{\argT}
\item{grid}{\argGrid}
\item{distances,dim}{\argDistances}
\item{...}{\argDots}
\item{data}{\argData}
\item{bin}{\argBin}
\item{phi}{\argPhi}
\item{theta}{\argTheta}
\item{deltaT}{\argDeltaT}
\item{vdim}{\argVdim}
}
\details{ \command{\link{RFpseudomadogram}} computes the empirical
pseudomadogram for given (multivariate) spatial data.
The spatial coordinates \code{x}, \code{y}, \code{z}
should be vectors. For random fields of
spatial dimension \eqn{d > 3} write all vectors as columns of matrix x. In
this case do neither use y, nor z and write the columns in
\code{gridtriple} notation.
If the data is spatially located on a grid a fast algorithm based on
the fast Fourier transformed (fft) will be used.
As advanced option the calculation method can also be changed for grid
data (see \command{\link{RFoptions}}.)
It is also possible to use \command{\link{RFpseudomadogram}} to calculate
the pseudomadogram (see \command{\link{RFoptions}}).
}
\value{
\command{\link{RFpseudomadogram}} returns objects of class
\command{\link[=RFempVariog-class]{RFempVariog}}.
}
\references{
Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp,
P. (eds.) (2010) \emph{Handbook of Spatial Statistics.}
Boca Raton: Chapman & Hall/CRL.
Stein, M. L. (1999) \emph{Interpolation of Spatial Data.}
New York: Springer-Verlag
}
\author{Jonas Auel; Sebastian Engelke; Johannes Martini; \martin}
\seealso{
\command{\link{RMstable}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}},
\command{\link{RFcov}},
\command{\link{RFmadogram}}.
\command{\link{RFvariogram}}.
}
\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 <- RMbiwm(nudiag=c(1, 2), nured=1, rhored=1, cdiag=c(1, 5),
s=c(1, 1, 2))
n <- 2
x <- seq(0, 20, 0.1)
z <- RFsimulate(model, x=x, y=x, n=n)
emp.vario <- RFpseudomadogram(data=z)
plot(emp.vario)
\dontshow{FinalizeExample()}}
\keyword{spatial}
\keyword{models}