
Replicated Poin t Patterns and Designed Experiments 691
0 5 10 15
0 2 4 6 8 10 14
x (mm)
ρ
(
x
)
ρ
^
(
x
)
ρ
hi
(
x
)
ρ
lo
(
x
)
Figure 16.20 . Estimated intensity of bronzefilter pattern as a function of x-coordinate.
0.0 0.2 0.4 0.6 0.8 1.0
0.0 1.0 2.0 3.0
left
r (mm)
K
inhom
(r)
0.0 0.2 0.4 0.6 0.8 1.0
0.0 1.0 2.0 3.0
right
r (mm)
K
inhom
(r)
Figure 1 6.21. Estimate s of the inhomogeneous K-function obtained from the left and right halves
of the bronze filter data.
Hahn and Jensen [ 311] propose a permutation test of the inhomogeneity assumption. The point
pattern is d ivided into quadrats, and the quadrats are organ ised into two groups representing high
and low intensity, respe ...