Considering intensity as a stochastic variable
Up to now, we have considered intensity as a fixed parameter of either:
- the whole study region \(A\) (homogeneous poisson process):
\[\lambda = \frac{E[N(A)]}{|A|}\]
- the location \(x\) (inhomogeneous poisson process):
\[\lambda(x) = \lim\limits_{|dx| \to 0}\frac{E[N(dx)]}{|dx|}\]