
464 Spatial Point Patterns: Methodology and Applications with R
Figure 12.15. Realisation of a Cauchy process with sca le
ω
= 0.1 (Left) and a variance- gamma
process with
ν
= 2 and scale
η
= 0.1 (Right) in the unit square. Open circles: offspring points.
Filled dots: parent points.
where
η
is the scale parameter and
ν
is an extra parameter controlling the ‘shape’ of the density,
which must satisfy
ν
> −1/2. Here Γ is the gamma function and K
ν
is the modified Bessel function
of the second kin d of order
ν
. The tails of the variance-gamma density are also heavy. A realisation
is shown in the right panel of Figure 12.15.
Comparison of cluster shapes
Figure 12.16 compar ...