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Bonferroni-type inequalities and the methods of indicators and polynomials

Published online by Cambridge University Press:  01 July 2016

Fred M. Hoppe  and
Eugene Seneta
Fred M. Hoppe*
Affiliation:
McMaster University
Eugene Seneta*
Affiliation:
University of Sydney
*
∗Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ont., L8S 4K1, Canada.
∗∗Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

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A difficulty in the application [5] of the method of polynomials as exposited by Galambos is investigated. The method, recast as the method of indicators, in a form due originally to Rényi [6], is applied to the situation of non-constant coefficients.

Keywords

MONOTONICITYNON-CONSTANT COEFFICIENTSSOBEL–UPPULURI INEQUALITIES
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 241 - 246
Copyright
Copyright © Applied Probability Trust 1990 

Footnotes

Research supported by NSERC.

Work done in part while on leave (1988–1989) at the Mathematics Department, University of Virginia.

References

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[3] Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York, N.Y.Google Scholar
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[6] Renyi, A. (1958) Quelques remarques sur les probabilités d'évènements dépendants. J. Math. Pures Appl. 37, 393–398.Google Scholar
[7] Sobel, M. and Uppuluri, V. R. R. (1972) On Bonferroni-type inequalities of the same degree for the probability of unions and intersections. Ann. Math. Statist. 43, 1549–1558.Google Scholar