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")