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Nonparametric estimation of the chord length distribution

Published online by Cambridge University Press:  01 July 2016

Martin B. Hansen*
Aalborg University
Erik W. van Zwet*
University of California, Berkeley
Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg Ø, Denmark. Email address:
∗∗ Postal address: University of California, Department of Statistics, 367 Evans Hall #3860, Berkeley, CA 94720-3860, USA.


The distribution of the length of a typical chord of a stationary random set is an interesting feature of the set's whole distribution. We give a nonparametric estimator of the chord length distribution and prove its strong consistency. We report on a simulation experiment in which our estimator compared favourably to a reduced sample estimator. Both estimators are illustrated by applying them to an image sample from a yoghurt ferment. We briefly discuss the closely related problem of estimation of the linear contact distribution. We show by a simulation experiment that a transformation of our estimator of the chord length distribution is more efficient than a Kaplan-Meier type estimator of the linear contact distribution.

MSC classification

Stochastic Geometry and Statistical Applications
Copyright © Applied Probability Trust 2001 

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