A spatial bivariate Poisson distribution

Abstract

SUMMARY A model for two associated Poisson processes on a plane is derived. The model generates a spatial bivariate Poisson process, the parameters of which depend in a simple manner on the parameters of the two individual processes, on the frequency of the joint occurrences and on the distance between the associated points. The nearest neighbour distribution for the distance between a point of one kind and its nearest neighbour of the second kind is obtained by simple considerations.