Lest: L-function

Description

Calculates an estimate of Ripley's L-function for a spatial point pattern.

Usage

Lest(...)

Arguments

...

Arguments passed to Kest to estimate the K-function.

Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv.
Essentially a data frame containing columns
rthe vector of values of the argument $r$ at which the function $L$ has been estimated
theothe 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.

Details

This command computes an estimate of the L-function for a spatial point pattern. The L-function is a transformation of Ripley's K-function, $$L(r) = \sqrt{\frac{K(r)}{\pi}}$$ where $K(r)$ is the K-function.

See Kest for information about Ripley's K-function.

The command Lest first calls Kest to compute the estimate of the K-function, and then applies the square root transformation.

For a completely random (uniform Poisson) point pattern, the theoretical value of the 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.

Examples

Run this code

data(cells)
 L <- Lest(cells)
 plot(L)
 plot(L, main="L function for cells")