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Variability orderings related to coverage problems on the circle

Published online by Cambridge University Press:  14 July 2016

Fred Huffer
Fred Huffer*
Affiliation:
The Florida State University
*
∗Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 32306, USA.
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Abstract

Suppose that n arcs with random lengths having distributions F1, F2, · ··, Fn are placed uniformly and independently on a circle. This paper presents inequalities which tell how certain distributions and probabilities change as the variability of the distributions Fl, F2, ··, Fn is increased. A distribution F is considered to be more variable than G if f h(x)dF(x) ≧ h(x)dG(x) for all convex functions h.

Keywords

GEOMETRICAL PROBABILITYRANDOM ARCS
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 97 - 106
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported by Office of Naval Research under contract N00014–76-C-0475.

References

Huffer, F. (1982) The Moments and Distributions of Some Quantities Arising from Random Arcs on the Circle. Ph.D. Dissertation, Department of Statistics, Stanford University.Google Scholar
Jewell, N. and Romano, J. (1982) Coverage problems and random convex hulls. J. Appl. Prob. 19, 546–561.CrossRefGoogle Scholar
Karlin, S. and Novikoff, A. (1963) Generalized convex inequalities. Pacific J. Math. 13, 1251–1279.Google Scholar
Ross, S. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Siegel, A. (1978) Random space filling and moments of coverage in geometrical probability. J. Appl. Prob. 15, 340–355.Google Scholar
Siegel, A. and Holst, L. (1982) Covering the circle with random arcs of random sizes. J. Appl. Prob. 19, 373–381.Google Scholar
Stoyan, D. (edited with revisions by D. J. Daley, (1983)) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Yadin, M. and Zacks, S. (1982) Random coverage of a circle with applications to a shadowing problem. J. Appl. Prob. 19, 562–577.Google Scholar