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A new metric between distributions of po A new metric between distributions of po... - PDF Document (378 K)
Citation
Schuhmacher, D. & Xia, A. (2008). A New metric between distributions of point processes. Advances in Applied Probability, 40(3), 651-672.
Title
A New metric between distributions of point processes
Author
Year
2008
Published in
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 d̅1 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 d̅1 and its induced Wasserstein metric d̅2 for point process distributions are given, including examples of useful d̅1-Lipschitz continuous functions, d̅2 upper bounds for the Poisson process approximation, and d̅2 upper 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 of d̅1 in applications.
Identifier
http://dx.doi.org/10.1239/aap/1222868180
Identifier
Schuhmacher, D. & Xia, A. (2008). A New metric between distributions of point processes. Advances in Applied Probability, 40(3), 651-672.
Identifier
0001-8678
Identifier
http://repository.uwa.edu.au:80/R/-?func=dbin-jump-full&object_id=10837&silo_library=GEN01
ISBN/ISSN
0001-8678
Subject
Department/School
Type
Journal article
Additional Information
Post print of work supplied
Link to Publisher's website supplied in Alternative Location.
Alternative Location
DOI
Persistent URL
http://repository.uwa.edu.au:80/R/-?func=dbin-jump-full&object_id=10837&silo_library=GEN01
Related collections
Engineering, Computing and Mathematics > Mathematics and Statistics