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On the length distribution of stochastic subarcs of a rectifiable arc

Published online by Cambridge University Press:  14 July 2016

J. E. Mann
J. E. Mann*
Affiliation:
Virginia Polytechnic Institute and State University
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Abstract

Suppose that A1, A2, · ··, An are disjoint subarcs of a rectifiable arc A ⊆ Rk. The location and length of each subarc are assumed to be continuous random variables. An expression for the expected fraction of A covered by subarcs each of length greater than τ ≧ 0 is obtained and applied to two conceptually distinct problems associated with light penetration of an absorbing medium.

Keywords

DISTRIBUTIONRECTIFIABLE ARCLIGHT PENETRATIONABSORBING MEDIUMFOLIAGE STRUCTURES
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 654 - 660
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Mann, J. E. and Curry, G. L. (1976) A sunfleck theory for general foliage location distributions. Biosystems Research Report, Department of Industrial Engineering, Texas A&M University.Google Scholar
[2] Miller, E. E. and Norman, J. M. (1971) A sunfleck theory for plant canopies I. Lengths of sunlit segments along a transect. Agron. J. 63, 735–738.Google Scholar
[3] Roelofs, R. (1950) Astronomy Applied to Land Surveying. N. V. Uitgeverij, Amsterdam.Google Scholar