bw.frac.Rd
\name{bw.frac}
\alias{bw.frac}
\title{
Bandwidth Selection Based on Window Geometry
}
\description{
Select a smoothing bandwidth for smoothing a point pattern,
based only on the geometry of the spatial window.
The bandwidth is a specified quantile of the distance
between two independent random points in the window.
}
\usage{
bw.frac(X, \dots, f=1/4)
}
\arguments{
\item{X}{
A window (object of class \code{"owin"}) or
point pattern (object of class \code{"ppp"})
or other data which can be converted to a window
using \code{\link{as.owin}}.
}
\item{\dots}{
Arguments passed to \code{\link{distcdf}}.
}
\item{f}{
Probability value (between 0 and 1)
determining the quantile of the distribution.
}
}
\details{
This function selects an appropriate bandwidth \code{sigma}
for the kernel estimator of point process intensity
computed by \code{\link{density.ppp}}.
The bandwidth \eqn{\sigma}{sigma} is computed as a
quantile of the distance between two independent random points
in the window. The default is the lower quartile of this
distribution.
If \eqn{F(r)} is the cumulative distribution function of the
distance between two independent random points uniformly distributed
in the window, then the value returned is the quantile
with probability \eqn{f}. That is, the bandwidth is
the value \eqn{r} such that \eqn{F(r) = f}.
The cumulative distribution function \eqn{F(r)} is
computed using \code{\link{distcdf}}. We then
we compute the smallest number \eqn{r}
such that \eqn{F(r) \ge f}{F(r) >= f}.
}
\value{
A numerical value giving the selected bandwidth.
The result also belongs to the class \code{"bw.frac"}
which can be plotted to show the cumulative distribution function
and the selected quantile.
}
\seealso{
\code{\link{density.ppp}},
\code{\link{bw.diggle}},
\code{\link{bw.relrisk}},
\code{\link{bw.scott}},
\code{\link{bw.smoothppp}},
\code{\link{bw.stoyan}}
}
\examples{
h <- bw.frac(letterR)
h
plot(h, main="bw.frac(letterR)")
}
\author{Adrian Baddeley
\email{Adrian.Baddeley@csiro.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{methods}
\keyword{smooth}