Analysing spatial point patterns in R - CSIRO

126 Distance methods for point patterns
> par(pty = "s")
> plot(Kest(cells))
Kest(cells)
K(r)
0.00 0.05 0.10 0.15 0.20
iso
trans
border
theo
0.00 0.05 0.10 0.15 0.20 0.25
r
In this case, the interpretation of all three summary statistics F, G and K is the same:
emphatic evidence of a regular pattern. It is not always the case that these three summaries
give equivalent messages.
A commonly-used transformation of K is the L-function
L(r) =
√
K(r)
which transforms the Poisson K function to the straight line L pois (r) = r, making visual assessment
of the graph much easier. The square root transformation also approximately stabilises
the variance of the estimator, making it easier to assess deviations.
To compute the estimated L function, use Lest.
> L plot(L, main = "L function")
π
L function
L(r)
0.00 0.05 0.10 0.15 0.20 0.25
iso
trans
border
theo
0.00 0.05 0.10 0.15 0.20 0.25
r
Another related summary function is the pair correlation function
CopyrightCSIRO 2010
g(r) = K′ (r)
2πr