Inhomogeneous L-function
Calculates an estimate of the inhomogeneous version of the L-function (Besag's transformation of Ripley's K-function) for a spatial point pattern.
Linhom(X, ..., correction)
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(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.
Essentially a data frame containing columns
r |
the vector of values of the argument r at which the function L has been estimated |
theo |
the theoretical value L(r) = r for a stationary Poisson process |
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Baddeley, A., Moller, J. and Waagepetersen, R. (2000) Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329–350.
data(japanesepines) X <- japanesepines L <- Linhom(X, sigma=0.1) plot(L, main="Inhomogeneous L function for Japanese Pines")
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