Analysing spatial point patterns in R - CSIRO

128 Distance methods for point patterns
19.5 J function
A useful combination of F and G is the J function [64]
J(r) = 1 − G(r)
1 − F(r)
(24)
defined for all r ≥ 0 such that F(r) < 1. For a homogeneous Poisson process, F pois = G pois , so
that
J pois (r) ≡ 1. (25)
Values J(r) > 1 suggest regularity, and J(r) < 1 suggest clustering.
An appealing property of the J function is that the superposition X • = X 1 ∪ X 2 of two
independent point processes X 1 ,X 2 has J-function
J(t) = λ 1
λ 1 + λ 2
J 1 (t) + λ 2
λ 1 + λ 2
J 2 (t)
where J 1 ,J 2 are the J-functions of X 1 ,X 2 respectively and λ 1 ,λ 2 are their intensities.
The J function is computed by Jest.
The convenient function allstats efficiently computes the F, G, J and K functions for a
dataset. They can be plotted automatically.
> plot(allstats(cells))
allstats(cells)
F function
G function
F(r)
0.0 0.2 0.4 0.6 0.8
km
rs
cs
theo
G(r)
0.0 0.2 0.4 0.6 0.8
km
rs
han
theo
0.00 0.02 0.04 0.06 0.08
0.00 0.05 0.10 0.15
r
r
J function
K function
J(r)
2 4 6 8
km
han
rs
theo
K(r)
0.00 0.05 0.10 0.15 0.20
iso
trans
border
theo
0.00 0.02 0.04 0.06 0.08
0.00 0.05 0.10 0.15 0.20 0.25
r
r
19.6 Manipulating and plotting summary functions
As explained above, the summary function commands Fest, Gest, Kest, Lest, pcf etc. return
a function value table (an object of class "fv"). This is a data frame (i.e. it also belongs to
the class "data.frame") with some extra information. One column of the data frame contains
CopyrightCSIRO 2010