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Sampling random polygons

Published online by Cambridge University Press:  14 July 2016

Edward I. George
Edward I. George*
Affiliation:
University of Chicago
*
∗ Postal address: Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637, USA.
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Abstract

Every realization of a Poisson line process is a set of lines which subdivides the plane into a population of non-overlapping convex polygons. To explore the unknown statistical features of this population, an alternative stochastic construction of random polygons is developed. This construction, which is based on an alternating sequence of random angles and side lengths, provides a fast simulation method for obtaining a random sample from the polygon population. For the isotropic case, this construction is used to obtain a random sample of 2500000 polygons, providing the most precise estimates to date of some of the unknown distributional characteristics.

Keywords

GEOMETRIC PROBABILITYPOISSON LINE PROCESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 557 - 573
Copyright
Copyright © Applied Probability Trust 1987 

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