
279Spatial Point Patterns
γ
γγ
()
()[()()] exp
h
c
h
a
h
h
=
+− −−
>
++
0001 0
0
2
2
when
when ==
0
(8.45)
It reaches the sill asymptotically as the exponential model. We dene the range as that distance
at which gamma is 95% of the sill as in Equation 8.41. It can be calculated from parameter a using
ha a
95
31732=×
. (8.46)
This is illustrated in Figure 8.20 for a = 3, c(0) = 1, γ(0
+
) = 0.2. In this case, the range is
h
95
331732
=×
≈.
8.10.4 linear anD poWer MoDels
The semivariance increases linearly with h and does not reach a maximum. This indicates a nonsta-
tionary variable. This is to say the variance does not reach a constant value, at l ...