Ldot.Rd
\name{Ldot}
\alias{Ldot}
\title{Multitype L-function (i-to-any)}
\description{
Calculates an estimate of the multitype L-function
(from type \code{i} to any type)
for a multitype point pattern.
}
\usage{
Ldot(X, i, ...)
}
\arguments{
\item{X}{The observed point pattern,
from which an estimate of the dot-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{\dots}{
Arguments passed to \code{\link{Kdot}}.
}
}
\details{
This command computes
\deqn{L_{i\bullet}(r) = \sqrt{\frac{K_{i\bullet}(r)}{\pi}}}{Li.(r) = sqrt(Ki.(r)/pi)}
where \eqn{K_{i\bullet}(r)}{Ki.(r)} is the multitype \eqn{K}-function
from points of type \code{i} to points of any type.
See \code{\link{Kdot}} for information
about \eqn{K_{i\bullet}(r)}{Ki.(r)}.
The command \code{Ldot} first calls
\code{\link{Kdot}} to compute the estimate of the \code{i}-to-any
\eqn{K}-function, and then applies the square root transformation.
For a marked Poisson point process,
the theoretical value of the L-function is
\eqn{L_{i\bullet}(r) = r}{Li.(r) = r}.
The square root also has the effect of stabilising
the variance of the estimator, so that \eqn{L_{i\bullet}}{Li.}
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_{i\bullet}}{Li.} has been estimated
}
\item{theo}{the theoretical value \eqn{L_{i\bullet}(r) = r}{Li.(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_{i\bullet}}{Li.}
obtained by the edge corrections named.
}
\seealso{
\code{\link{Kdot}},
\code{\link{Lcross}},
\code{\link{Lest}}
}
\examples{
data(amacrine)
L <- Ldot(amacrine, "off")
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}