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Intercept lengths of random probes through boxes

Published online by Cambridge University Press:  14 July 2016

Rodney Coleman
Rodney Coleman*
Affiliation:
Imperial College, London
*
∗Postal address: Department of Mathematics, Imperial College, Huxley Building, Queen's Gate, London SW7 2BZ, U.K.
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Abstract

The distribution and its moments are given of the length of the intercept made by a random probe through a box having perpendicular edge lengths a, b and c. Three types of random probe are considered.

Keywords

STEREOLOGYGEOMETRICAL PROBABILITYRANDOM SECANTSRANDOM CHORDSPARALLELEPIPED
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 276 - 282
Copyright
Copyright © Applied Probability Trust 

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References

Coleman, R. (1969) Random paths through convex bodies. J. Appl. Prob. 6, 430–441.CrossRefGoogle Scholar
Coleman, R. (1973) Random paths through rectangles and cubes. Metallography 6, 103–114.CrossRefGoogle Scholar
Coleman, R. (1979) An introduction to mathematical stereology. Memoir Series, Department of Theoretical Statistics, Institute of Mathematics, Aarhus University, Denmark.Google Scholar
Duvaljan, A. V. (1970) Zavodskaja Laboratorija 36, 1200–1204. (See Saltykov, S. A. (1974), p. 299).Google Scholar
Enns, E. G. and Ehlers, P. F. (1978) Random paths through a convex region. J. Appl. Prob. 15, 144–152.CrossRefGoogle Scholar
Horowitz, M. (1965) Probability of random paths across elementary geometrical shapes. J. Appl. Prob. 2, 169–177.CrossRefGoogle Scholar
Kellerer, A. M. (1971) Considerations on the random traversal of convex bodies and solutions for general cylinders. Radiation Res. 47, 359–376.CrossRefGoogle ScholarPubMed
Naumovitch, N. M. and Warren, R. (1978) Influence of particle shape and spatial size distribution on random intercept length distributions. In Quantitative Analysis of Microstructures in Materials Science, Biology and Medicine, ed. Chermant, J. L. (Special Issue No. 8 of Practical Metallography), Dr. Riederer-Verlag, Stuttgart, 161–170.Google Scholar
Saltykov, S. A. (1974) Stereometrische Metallographie. VEB Deutscher Verlag für Grundstoffindustrie, Leipzig.Google Scholar
Warren, R. and Naumovitch, N. (1977) Relative frequencies of random intercepts through convex bodies. J. Microsc. 110, 113–120.CrossRefGoogle Scholar