The Entropy of a Point Process

Abstract

In this paper the entropy of a point process is defined. This entropy can be expressed as a sum of two terms: (a) the numerical entropy, associated with the number of events in a fixed interval, and (b) the locational entropy, associated with the locations of those events in the interval. For point processes describable as a generalized birth process, with fixed intensity function, the rate of change of entropy at a given time is a maximum for the inhomogeneous Poisson process. For the mixed Poisson process with fixed intensity, the locational entropy for a given interval is a maximum for the Poisson process. Other properties of the numerical and locational entropies are also discussed.