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Random coverage of the circle and asymptotic distributions

Published online by Cambridge University Press:  14 July 2016

J. Hüsler
J. Hüsler*
Affiliation:
University of Bern
*
∗Postal address: Department of Mathematical Statistics, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland.
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Abstract

Place n arcs of equal length an uniformly at random on the circumference of a circle. We discuss the limiting distributions of the number of gaps, the length of the maximum gap and the uncovered proportion of the circle, depending on the asymptotic behaviour of an → 0.

Keywords

ASYMPTOTIC DISTRIBUTIONSRANDOM ARCSGEOMETRICAL PROBABILITYMAXIMUM GAPNUMBER OF GAPS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 578 - 587
Copyright
Copyright © Applied Probability Trust 1982 

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References

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