The cluster strength index of a cluster process model or Cox process model
is a numerical index which expresses the strength of clustering.
It is defined as (Baddeley et al., 2022, section 10.2)
$$
\varphi = g(0)-1
$$
where \(g\) is the pair correlation function of the
cluster process.
The index \(\varphi\) is dimensionless and takes
non-negative values. Values close to zero indicate that the
process is close to a Poisson process.
For a cluster process, \(\varphi\) is related to the
sibling probability \(p\) by
\(p = \varphi/(1+\varphi)\).
For a Cox process with driving random intensity
\(\Lambda(x)\),
$$
\varphi = \frac{\mbox{var}(\Lambda(0))}{E[\Lambda(0)]^2}
$$
is a measure of the variability of the random intensity.