On Some Characteristics of Anisotropic Fibre Processes

This paper derives properties of various estimators of length intensity of stationary random fibre processes in Rd. The projections of the process onto R1 and intersections with a system of parallel (d ‐ 1)‐dimensional hyperplanes are studied. The estimation variances are expressed by means of pair...

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Bibliographic Details
Published in:Mathematische Nachrichten 1994, Vol.169 (1), p.5-17
Main Authors: Beneš, Viktor, Chadœuf, Joël, Ohser, Joachim
Format: Article
Language:English
Subjects:
Life Sciences
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Summary:This paper derives properties of various estimators of length intensity of stationary random fibre processes in Rd. The projections of the process onto R1 and intersections with a system of parallel (d ‐ 1)‐dimensional hyperplanes are studied. The estimation variances are expressed by means of pair correlation functions of appropriate random measures. The results are formulated for the anisotropic models in arbitrary dimension. Explicit formulas are obtained for the anistropic Boolean segment process.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.19941690102