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Maximal, non-uniform spacings and the coverage problem

Published online by Cambridge University Press:  14 July 2016

Jürg Hüsler
Jürg Hüsler*
Affiliation:
University of Bern
*
∗ Department of Math. Statistics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
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Abstract

The spacings have been widely applied to many situations, such as for example the coverage problem of the circle or the line, under the hypothesis of uniformity. The paper examines the asymptotic behaviour of the maximal spacings under non-uniformity, assuming that the existing density f has a minimum point m with f(m) = 0. The results are applied to the coverage of the circle by randomly placed arcs.

Keywords

SPACINGSORDER STATISTICSGAPSVACANCYLIMIT LAWS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 519 - 528
Copyright
Copyright © Applied Probability Trust 1988 

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References

David, H. (1981) Order Statistics, 2nd edn. Wiley, New York.Google Scholar
Deheuvels, P. (1986) On the influence of the extremes of an i.i.d. sequence on the maximal spacings. Ann. Prob. 14, 194–208.Google Scholar
De Haan, L. (1970) On Regular Variation and its Application to the Weak Convergence of Sample Extremes. Mathematical Centre Tracts 32, Amsterdam.Google Scholar
Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
Hall, P. (1984) Random, nonuniform distribution of line segments on a circle. Stoch. Proc. Appl. 18, 239–261.Google Scholar
Holst, L. and Hüsler, J. (1984) On the random coverage of the circle. J. Appl. Prob. 21, 558–566.Google Scholar
Hüsler, J. (1982) Random coverage of the circle and asymptotic distributions. J. Appl. Prob. 19, 578–587.Google Scholar
Leadbetter, M. R., Lindgren, G. and Rootzén, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York.Google Scholar