Linhom
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.
- Keywords
- spatial, nonparametric
Usage
Linhom(...)
Arguments
- ...
- Arguments passed to
Kinhom
to estimate the inhomogeneous K-function.
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"
, seefv.object
, which can be plotted directly usingplot.fv
.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.
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
data(japanesepines)
X <- japanesepines
L <- Linhom(X, sigma=0.1)
plot(L, main="Inhomogeneous L function for Japanese Pines")