Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T11:37:55.773Z Has data issue: false hasContentIssue false

On the length distribution of stochastic subarcs of a rectifiable arc

Published online by Cambridge University Press:  14 July 2016

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

Abstract

Suppose that A1, A2, · ··, An are disjoint subarcs of a rectifiable arc ARk. 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.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1977 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 735738.Google Scholar
[3] Roelofs, R. (1950) Astronomy Applied to Land Surveying. N. V. Uitgeverij, Amsterdam.Google Scholar