ABSTRACT
Data were collected at fixed locations or regions. Sometimes the locations at which events occur are random. Typical examples include the epicentres of earthquakes or the outbreaks of forest fires. Such random configurations of locations are said to form a point process. Recall that the Poisson distribution arises as the limit of binomial distributions with ever more trials having ever smaller success probabilities. The same idea applies to binomial point processes. The moments are important descriptors of random variables, as are the mean and covariance functions of random fields. For point processes, their analogues are the moment measures. A cluster process is defined in two steps. In the first step, sample a ‘parent’ point process. Secondly, conditionally on the parents, let each of them generate a new point process of ‘daughters’ and take the superposition of all daughters.
