A new metric between distributions of point processes

Details A new metric between distributions of point processes A new metric between distributions of point processes

2007-08-21

arxiv.org/abs/0708.2777v1

Mathematics

Probability

20 pages, 2 figures

Scientific paper

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 $\bar{d}_1$ 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 $\bar{d}_1$ and its induced Wasserstein metric $\bar{d}_2$ for point process distributions are given, including examples of useful $\bar{d}_1$-Lipschitz continuous functions, $\bar{d}_2$ upper bounds for Poisson process approximation, and $\bar{d}_2$ upper and lower bounds between distributions of point processes of i.i.d. points. Furthermore, we present a statistical test for multiple point pattern data that demonstrates the potential of $\bar{d}_1$ in applications.

Affiliated with

Also associated with

No associations

Rating

A new metric between distributions of point processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A new metric between distributions of point processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new metric between distributions of point processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-366841