Linhom(...)Kinhom
to estimate the inhomogeneous K-function.
"fv", see fv.object,
which can be plotted directly using plot.fv.Essentially a data frame containing columnstogether 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.
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.
Kest,
Lest,
Kinhom,
pcf
data(japanesepines)
X <- japanesepines
L <- Linhom(X, sigma=0.1)
plot(L, main="Inhomogeneous L function for Japanese Pines")
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