| Linhom {spatstat.explore} | R Documentation |
Inhomogeneous L-function
Description
Calculates an estimate of the inhomogeneous version of
the L-function (Besag's transformation of Ripley's K-function)
for a spatial point pattern.
Usage
Linhom(X, ..., correction)
Arguments
X |
The observed point pattern,
from which an estimate of |
correction, ... |
Other arguments passed to |
Details
This command computes an estimate of the inhomogeneous version of
the L-function for a spatial point pattern.
The original L-function is a transformation
(proposed by Besag) of Ripley's K-function,
L(r) = \sqrt{\frac{K(r)}{\pi}}
where K(r) is the Ripley K-function of a spatially homogeneous
point pattern, estimated by Kest.
The inhomogeneous L-function is the corresponding transformation
of the inhomogeneous K-function, estimated by Kinhom.
It is appropriate when the point pattern clearly does not have a
homogeneous intensity of points. It was proposed by
Baddeley, Moller and Waagepetersen (2000).
The command Linhom first calls
Kinhom to compute the estimate of the inhomogeneous K-function,
and then applies the square root transformation.
For a Poisson point pattern (homogeneous or inhomogeneous),
the theoretical value of the inhomogeneous L-function is L(r) = r.
The square root also has the effect of stabilising
the variance of the estimator, so that L is more appropriate
for use in simulation envelopes and hypothesis tests.
Value
An object of class "fv", see fv.object,
which can be plotted directly using plot.fv.
Essentially a data frame containing columns
r |
the vector of values of the argument |
theo |
the theoretical value |
together with columns named
"border", "bord.modif",
"iso" and/or "trans",
according to the selected edge corrections. These columns contain
estimates of the function L(r) obtained by the edge corrections
named.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner rolfturner@posteo.net
References
Baddeley, A., Moller, J. and Waagepetersen, R. (2000) Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329–350.
See Also
Examples
X <- japanesepines
L <- Linhom(X, sigma=0.1)
plot(L, main="Inhomogeneous L function for Japanese Pines")