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Random secants of a convex body generated by surface randomness

Published online by Cambridge University Press:  14 July 2016

P. Frank Ehlers  and
Ernest G. Enns
P. Frank Ehlers
Affiliation:
Okanagan College
Ernest G. Enns
Affiliation:
University of Calgary
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Abstract

Length distributions for random secants through a convex region K are derived for three types of randomness. The results are formulated in terms of geometric properties of K, e.g. the overlap surface content of K with its translated self. The distribution of distance between two random points in K, expressed in terms of the overlap volume, is shown to extend to non-convex (including disjoint) regions.

Keywords

GEOMETRICAL PROBABILITYCONVEXITYRANDOM SECANTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 157 - 166
Copyright
Copyright © Applied Probability Trust 

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References

Alagar, V. S. (1976) The distribution of the distance between random points. J. Appl. Prob. 13, 558–566.Google Scholar
Coleman, R. (1969) Random paths through convex bodies. J. Appl. Prob. 6, 430–441.Google Scholar
Enns, E. G. and Ehlers, P. F. (1978) Random paths through a convex region. J. Appl. Prob. 15, 144–152.Google Scholar
Enns, E. G. and Ehlers, P. F. (1980) Random paths originating within a convex region and terminating on its surface. Austral. J. Statist. 22, 60–68.Google Scholar
Kingman, J. F. C. (1969) Random secants of a convex body. J. Appl. Prob. 6, 660–672.Google Scholar
Ruben, H. (1978) On the distance between points in polygons. In Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, ed. Miles, R. E. and Serra, J., Springer-Verlag, Berlin, 49–69.Google Scholar