
Correlation 249
7.12 Third- and higher-order summary statisti cs
We saw on page 211 that two different point processes can have identical first-order (intensity) and
second-order (correlatio n) properties. In order to distinguish between such processes we need an-
other ap proach. One possible strategy is to estimate the third-order moments, which would involve
counting triples rath e r than pairs of data poin ts.
For a stationary point process X with intensity
λ
, the triangle -counting f unction T (r) is define d
as the n ormalised expected number of triangles formed by points of X, with all side len gths less
than or equal to r, with one corner at