A new metric between distributions of point processes

Abstract

Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric d̄1 that combines positional differences of points under a closest match with the relative difference in total mass in a way that fixes this flaw. A comprehensive collection of theoretical results about d̄1 and its induced Wasserstein metric d̄2 for point process distributions are given, including examples of useful d̄1-Lipschitz continuous functions, d̄2 upper bounds for the Poisson process approximation, and d̄2 upper and lower bounds between distributions of point processes of inde..