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 metricd̅1that 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 aboutd̅1and its induced Wasserstein metricd̅2for point process distributions are given, including examples of usefuld̅1-Lipschitz continuous functions,d̅2upper bounds for the Poisson process approximation, andd̅2upper and lower bounds between distributions of point processes of independent and identically distributed points. Furthermore, we present a statistical test for multiple point pattern data that demonstrates the potential ofd̅1in applications.
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