Analysing spatial point patterns in R - CSIRO

31.3 Distance methods and summary functions 191
> data(amacrine)
> amacrine
> plot(Gcross(amacrine, "on", "off"))
Gcross(amacrine, "on", "off")
Gcross on, off(r)
0.0 0.2 0.4 0.6 0.8
km
rs
han
theo
0.00 0.01 0.02 0.03 0.04 0.05 0.06
r (one unit = 662 microns)
The interpretation of the cross-type summary functions is similar, but not identical, to that
of the original functions F, G, K etc:
if X j is a uniform Poisson process (CSR), then F j (r) = 1 − exp(−λ j πr 2 ).
if X j is a uniform Poisson process (CSR) and is independent of X i , then G ij (r) = 1 −
exp(−λ j πr 2 ).
if X i and X j are independent, then K ij (r) = πr 2 , L ij (r) = r, g ij (r) = 1, G ij (r) = F ij (r)
and J ij (r) = 1.
Here ‘independent’ means that the two point processes are probabilistically independent.
31.3.2 All pairs of types
The command alltypes enables the user to compute the cross-type summary functions between
all pairs of types simultaneously. For example, to compute G ij (r) for all i and j in the amacrine
cells data, we would use alltypes(amacrine, "G"). The result is automatically displayed as
an array of plot panels.
> plot(alltypes(amacrine, "G"))
CopyrightCSIRO 2010