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On the moments of vacancy of random arcs on the circle

Published online by Cambridge University Press:  14 July 2016

Norbert Henze
Norbert Henze*
Affiliation:
University of Hanover
*
∗Postal address: Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, D-3000 Hannover 1, West Germany.
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Abstract

Place n arcs of equal length uniformly at random on the circumference of a circle. We give a simple probabilistic derivation of the moments of the uncovered portion of the circle.

Keywords

RANDOM COVERING OF THE CIRCLEMOMENTS OF COVERAGE
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 837 - 840
Copyright
Copyright © Applied Probability Trust 1986 

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References

Holst, L. (1983) A note on random arcs on the circle. In Probability and Mathematical Statistics, Essays in Honour of C. G. Esséen, Uppsala University, 40–46.Google Scholar
Holst, L. and Hülser, J. (1984) On the random coverage of the circle. J. Appl. Prob. 21, 558–566.Google Scholar
Johnson, N. L. and Kotz, S. (1977) Urn Models and their Applications. Wiley, New York.Google Scholar
Robbins, H. E. (1944) On the measure of a random set. Ann. Math. Statist. 15, 70–74.Google Scholar
Siegel, A. F. (1978) Random arcs on the circle. J. Appl. Prob. 15, 774–789.Google Scholar