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Second-order stereology for planar fibre processes

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

V. Weiss  and
W. Nagel
V. Weiss
Affiliation:
Friedrich-Schiller-Universität, Jena
W. Nagel*
Affiliation:
Friedrich-Schiller-Universität, Jena
*
* Postal address for both authors: Friedrich-Schiller-Universität, Fakultät für Mathematik und Informatik, 07740 Jena, Germany.
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Abstract

Three different stereological methods for the determination of second-order quantities of planar fibre processes which have been suggested in the literature are considered. Proofs of the formulae are given (also by using a new integral geometric formula), relations between the methods are derived and the prerequisites are discussed. Furthermore, edge-corrected unbiased estimators for the second-order quantities are given.

Keywords

STOCHASTIC GEOMETRYINTEGRAL GEOMETRYSECOND-ORDER QUANTITYEDGE EFFECT CORRECTION

MSC classification

Primary: 60G99: None of the above, but in this section
Secondary: 60G12: General second-order processes 60D05: Geometric probability and stochastic geometry
Type
Research Article
Information
Advances in Applied Probability , Volume 26 , Issue 4 , December 1994 , pp. 906 - 918
Copyright
Copyright © Applied Probability Trust 1994 

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