In this paper we develop maximum likelihood procedures for parameter estimation and model selection that apply to a large class of point process models that have been used to model rainfall occurrences, including Cox processes, Neyman‐Scott processes, and renewal processes. The statistical inference procedures are based on the stochastic intensity λ(t) = lims→0,s>0(1/s)E[N(t + s) −N(t)|N(u),u