586 Spatial Point Patterns: Methodology and Applications with R
3.
If the process has constant relative risk, i.e.
λ
m
(u) = p
m
λ
•
(u), then independent
labelling (MPP2
′
) implies completely rando m labelling (MPP2).
4. If (MPP2) and (MPP4) hold [sic], then the process is a multitype Poisson process.
The last statement say s that if a multitype point process has completely random labelling, and
indepen dent compone nts, then it is a multitype Poisson process. It must nece ssarily also have
constant relative risk,
λ
m
(u) = p
m
λ
•
(u). Thus, the properties of completely rand om labelling and
indepen dence of components, if we could verify them both, are enough to establish that the point
process is Po isson. However, an inhomogeneous m ultitype Poisson proce ss ...