Correlation 209
randomly added, combined, disp la ced, or removed. In this regard there a re two important properties
of the K-function.
Firstly the K-function is invariant under random thinning. Suppose X is a stationary point
process, and Y is the point process obtained by ind e pendent ran dom thinning — randomly deleting
or retaining each point of X, with a constan t probability p of retaining each p oint (Section 5.3.3).
Then the K-function of Y is ide ntical to th e K-function of X.
Secondly there is the effect of superposition. Suppose X and Y are two independent, stationary
point processes, with intensities
λ
X
,
λ
Y
and K-functio ns K
X
(r),K
Y
(r). Superimposing these two
processes gives a stationary point process with intensity
λ
=
λ
X
+
λ
Y
and K-function ...