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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
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