ON THE ESTIMATION OF DISTANCE DISTRIBUTION FUNCTIONS FOR POINT PROCESSES AND RANDOM SETS

Dietrich Stoyan, Helga Stoyan, André Tscheschel, Torsten Mattfeldt

Abstract

This paper discusses various estimators for the nearest neighbour distance distribution function D of a stationary point process and for the quadratic contact distribution function Hq of a stationary random closed set. It recommends the use of Hanisch's estimator of D, which is of Horvitz-Thompson type, and the minussampling estimator of Hq. This recommendation is based on simulations for Poisson processes and Boolean models.

Keywords
contact distribution; Horvitz-Thompson; estimator; minus-sampling; nearest neighbour distance distribution

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DOI: 10.5566/ias.v20.p65-69

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)