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On Some Characteristics of Anisotropic Fibre Processes
Author(s) -
Beneš Viktor,
Chadœuf Joël,
Ohser Joachim
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941690102
Subject(s) - mathematics , hyperplane , anisotropy , estimator , boolean model , dimension (graph theory) , intensity (physics) , process (computing) , combinatorics , mathematical analysis , statistical physics , discrete mathematics , statistics , optics , computer science , physics , operating system
This paper derives properties of various estimators of length intensity of stationary random fibre processes in R d. The projections of the process onto R 1 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.