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\name{linearpcf}
\alias{linearpcf}
\title{
Linear Pair Correlation Function
}
\description{
Computes an estimate of the linear pair correlation function
for a point pattern on a linear network.
}
\usage{
linearpcf(X, r=NULL, ..., correction="Ang", ratio=FALSE)
}
\arguments{
\item{X}{
Point pattern on linear network (object of class \code{"lpp"}).
}
\item{r}{
Optional. Numeric vector of values of the function argument \eqn{r}.
There is a sensible default.
}
\item{\dots}{
Arguments passed to \code{\link{density.default}}
to control the smoothing.
}
\item{correction}{
Geometry correction.
Either \code{"none"} or \code{"Ang"}. See Details.
}
\item{ratio}{
Logical.
If \code{TRUE}, the numerator and denominator of
each estimate will also be saved,
for use in analysing replicated point patterns.
}
}
\details{
This command computes the linear pair correlation function
from point pattern data on a linear network.
The pair correlation function is estimated from the
shortest-path distances between each pair of data points,
using the fixed-bandwidth kernel smoother
\code{\link{density.default}},
with a bias correction at each end of the interval of \eqn{r} values.
To switch off the bias correction, set \code{endcorrect=FALSE}.
The bandwidth for smoothing the pairwise distances
is determined by arguments \code{\dots}
passed to \code{\link{density.default}}, mainly the arguments
\code{bw} and \code{adjust}. The default is
to choose the bandwidth by Silverman's rule of thumb
\code{bw="nrd0"} explained in \code{\link{density.default}}.
If \code{correction="none"}, the calculations do not include
any correction for the geometry of the linear network. The result is
an estimate of the first derivative of the
network \eqn{K} function defined by Okabe and Yamada (2001).
If \code{correction="Ang"}, the pair counts are weighted using
Ang's correction (Ang, 2010). The result is an estimate of the
pair correlation function in the linear network.
}
\value{
Function value table (object of class \code{"fv"}).
If \code{ratio=TRUE} then the return value also has two
attributes called \code{"numerator"} and \code{"denominator"}
which are \code{"fv"} objects
containing the numerators and denominators of each
estimate of \eqn{g(r)}.
}
\author{
\wei and
\adrian.
}
\references{
Ang, Q.W. (2010) Statistical methodology for spatial point patterns
on a linear network. MSc thesis, University of Western Australia.
Ang, Q.W., Baddeley, A. and Nair, G. (2012)
Geometrically corrected second-order analysis of
events on a linear network, with applications to
ecology and criminology.
\emph{Scandinavian Journal of Statistics} \bold{39}, 591--617.
Okabe, A. and Yamada, I. (2001) The K-function method on a network and
its computational implementation. \emph{Geographical Analysis}
\bold{33}, 271-290.
}
\seealso{
\code{\link{linearK}},
\code{\link{linearpcfinhom}},
\code{\link{lpp}}
}
\examples{
X <- rpoislpp(5, simplenet)
linearpcf(X)
linearpcf(X, correction="none")
}
\keyword{spatial}
\keyword{nonparametric}
\concept{Linear network}
|
