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(...)Arguments passed to Kinhom
to estimate the inhomogeneous K-function.
An object of class "fv", see fv.object,
which can be plotted directly using plot.fv.
Essentially a data frame containing columns
the vector of values of the argument \(r\) at which the function \(L\) has been estimated
the theoretical value \(L(r) = r\) for a stationary Poisson process
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.
Baddeley, A., Moller, J. and Waagepetersen, R. (2000) Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329--350.
# NOT RUN {
data(japanesepines)
X <- japanesepines
L <- Linhom(X, sigma=0.1)
plot(L, main="Inhomogeneous L function for Japanese Pines")
# }
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