Intensity function of a spatial point process

Intensity of a spatial point pattern: number of events per unit area.

\[\lambda = \frac{N(A)}{|A|}\]

For a spatial point process, \(N(A)\) is a random variable, so its expected value is used to define the intensity parameter \(\lambda\):

\[\lambda = \frac{E[N(A)]}{|A|}\]