
Point Patterns on a Linear Network 739
0 200 400 600 800 1000
0 5000 10000 15000
r (mm)
K
net
(
r
)
Figure 17.18. Okabe-Yamada network K-fun c tion for the spider web data (solid black lines) and
the sample mean (dashed lines) and pointwise envelopes (boundary of shaded region) of the same
function for 39 simulations of a homogeneous Poisson process on the sa m e network.
On a lin e ar network, we will need to make analogous assumptions in order to define the K-
function. Unfortunately the concept of a (fully) stationary point pr ocess is meaningless on a linear
network, because the network itself is not homogeneous: different locations in the network are ...