Revision 9ed6d6be90c4a866357a121a3f106a0bea1cdb99 authored by Adrian Baddeley on 22 July 2008, 00:00:00 UTC, committed by Gabor Csardi on 22 July 2008, 00:00:00 UTC
1 parent f919f46
Lcross.Rd
\name{Lcross}
\alias{Lcross}
\title{Multitype L-function (cross-type)}
\description{
Calculates an estimate of the cross-type L-function
for a multitype point pattern.
}
\usage{
Lcross(X, i, j, ...)
}
\arguments{
\item{X}{The observed point pattern,
from which an estimate of the cross-type \eqn{L} function
\eqn{L_{ij}(r)}{Lij(r)} will be computed.
It must be a multitype point pattern (a marked point pattern
whose marks are a factor). See under Details.
}
\item{i}{Number or character string identifying the type (mark value)
of the points in \code{X} from which distances are measured.
}
\item{j}{Number or character string identifying the type (mark value)
of the points in \code{X} to which distances are measured.
}
\item{\dots}{
Arguments passed to \code{\link{Kcross}}.
}
}
\details{
The cross-type L-function is a transformation of the cross-type K-function,
\deqn{L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}}{Lij(r) = sqrt(Kij(r)/pi)}
where \eqn{K_{ij}(r)}{Kij(r)} is the cross-type K-function
from type \code{i} to type \code{j}.
See \code{\link{Kcross}} for information
about the cross-type K-function.
The command \code{Lcross} first calls
\code{\link{Kcross}} to compute the estimate of the cross-type K-function,
and then applies the square root transformation.
For a marked point pattern in which the points of type \code{i}
are independent of the points of type \code{j},
the theoretical value of the L-function is
\eqn{L_{ij}(r) = r}{Lij(r) = r}.
The square root also has the effect of stabilising
the variance of the estimator, so that \code{L_{ij}}{Lij} is more appropriate
for use in simulation envelopes and hypothesis tests.
}
\value{
An object of class \code{"fv"}, see \code{\link{fv.object}},
which can be plotted directly using \code{\link{plot.fv}}.
Essentially a data frame containing columns
\item{r}{the vector of values of the argument \eqn{r}
at which the function \eqn{L_{ij}}{Lij} has been estimated
}
\item{theo}{the theoretical value \eqn{L_{ij}(r) = r}{Lij(r) = r}
for a stationary Poisson process
}
together with columns named
\code{"border"}, \code{"bord.modif"},
\code{"iso"} and/or \code{"trans"},
according to the selected edge corrections. These columns contain
estimates of the function \eqn{L_{ij}}{Lij} obtained by the edge corrections
named.
}
\seealso{
\code{\link{Kcross}},
\code{\link{Ldot}},
\code{\link{Lest}}
}
\examples{
data(amacrine)
L <- Lcross(amacrine, "off", "on")
plot(L)
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{nonparametric}
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