Revision 2cce766bb3e656de2c829da29ab8c51681004900 authored by Adrian Baddeley on 11 November 2010, 00:00:00 UTC, committed by Gabor Csardi on 11 November 2010, 00:00:00 UTC
1 parent 6bd38f3
Gfox.Rd
\name{Gfox}
\alias{Gfox}
\alias{Jfox}
\title{
Foxall's Distance Functions
}
\description{
Given a point pattern \code{X} and a spatial object \code{Y},
compute estimates of Foxall's \eqn{G} and \eqn{J} functions.
}
\usage{
Gfox(X, Y, r = NULL, breaks = NULL, correction = c("km", "rs", "han"), ...)
Jfox(X, Y, r = NULL, breaks = NULL, correction = c("km", "rs", "han"), ...)
}
\arguments{
\item{X}{
A point pattern (object of class \code{"ppp"})
from which distances will be measured.
}
\item{Y}{
An object of class \code{"ppp"}, \code{"psp"} or \code{"owin"}
to which distances will be measured.
}
\item{r}{Optional. Numeric vector. The values of the argument \eqn{r}
at which \eqn{Gfox(r)} or \eqn{Jfox(r)}
should be evaluated. There is a sensible default.
First-time users are strongly advised not to specify this argument.
See below for important conditions on \eqn{r}.
}
\item{breaks}{An alternative to the argument \code{r}.
Not normally invoked by the user.
}
\item{correction}{
Optional.
The edge correction(s) to be used to estimate
\eqn{Gfox(r)} or \eqn{Jfox(r)}.
A vector of character strings selected from
\code{"none"}, \code{"rs"}, \code{"km"}, \code{"cs"}
and \code{"best"}.
}
\item{\dots}{
Extra arguments affecting the discretisation of distances.
These arguments are ignored by \code{Gfox}, but
\code{Jfox} passes them to \code{\link{Hest}} to determine
the discretisation of the spatial domain.
}
}
\details{
Given a point pattern \code{X} and another spatial object \code{Y},
these functions compute two nonparametric measures of association
between \code{X} and \code{Y}, introduced by Foxall
(Foxall and Baddeley, 2002).
Let the random variable \eqn{R} be the distance from a typical point
of \code{X} to the object \code{Y}.
Foxall's \eqn{G}-function is the cumulative distribution function
of \eqn{R}:
\deqn{G(r) = P(R \le r)}{P(R <= r)}
Let the random variable \eqn{S} be the distance from a \emph{fixed} point
in space to the object \code{Y}. The cumulative distribution function
of \eqn{S} is the (unconditional) spherical contact distribution
function
\deqn{H(r) = P(S \le r)}{H(r) = P(S <= r)}
which is computed by \code{\link{Hest}}.
Foxall's \eqn{J}-function is the ratio
\deqn{
J(r) = \frac{1-G(r)}{1-H(r)}
}{
J(r) = (1-G(r))/(1-H(r))
}
For further interpretation, see Foxall and Baddeley (2002).
}
\value{
A function value table (object of class \code{"fv"})
which can be printed, plotted, or converted to a data frame of values.
}
\references{
Foxall, R. and Baddeley, A. (2002)
Nonparametric measures of association between a
spatial point process and a random set, with
geological applications. \emph{Applied Statistics} \bold{51}, 165--182.
}
\seealso{
\code{\link{Gest}},
\code{\link{Hest}},
\code{\link{Jest}},
\code{\link{Fest}}
}
\examples{
data(copper)
X <- copper$SouthPoints
Y <- copper$SouthLines
G <- Gfox(X,Y)
J <- Jfox(X,Y, correction="km")
}
\author{Rob Foxall and
Adrian Baddeley
\email{Adrian.Baddeley@csiro.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
}
\keyword{spatial}
\keyword{nonparametric}
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