Analysing spatial point patterns in R - CSIRO

25.2 Inhomogeneous cluster models 151
lty col key label
bord.modif 1 1 bord.modif K[bordm](r)
border 2 2 border K[bord](r)
theo 3 3 theo K[pois](r)
meaning
bord.modif modified border-corrected estimate of K(r)
border border-corrected estimate of K(r)
theo
theoretical Poisson K(r)
(the smoothing parameter σ can also be controlled.)
The inhomogeneous analogue of the L-function is defined by
̂L inhom (r) =
√
1
π ̂K inhom (r)
This can be computed using Linhom. For an inhomogeneous Poisson process, L inhom (r) ≡ r.
The inhomogeneous analogue of the pair correlation function can be defined, similarly to the
homogeneous case, as
g inhom (r) = K′ inhom (r) .
2πr
It has the same interpretation, namely, that g inhom (r) is the probability of observing a pair of
points at certain locations separated by a distance r, divided by the corresponding probability
for a Poisson process of the same (inhomogeneous) intensity.
The inhomogeneous pair correlation function is computed by pcfinhom:
> g g