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Multivariate Bonferroni-type lower bounds

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Tuhao Chen  and
E. Seneta
Tuhao Chen*
Affiliation:
University of Sydney
E. Seneta*
Affiliation:
University of Sydney
*
∗Postal address for both authors: School of Mathematics and Statistics, F07, University of Sydney, N.S.W. 2006, Australia.
∗Postal address for both authors: School of Mathematics and Statistics, F07, University of Sydney, N.S.W. 2006, Australia.
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Abstract

We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at least a1 and at least a2, and for the probability that exactly a1 and a2, out of n and N events, occur. The lower bound presented here reduces to a sharper bound than that of Galambos and Lee (1992). Our approach is by way of indicator functions and bivariate binomial moments. A new concept, marginal Bonferroni summation, is introduced in this paper.

Keywords

BIVARIATE BINOMIAL MOMENTSINDICATOR FUNCTIONSMARGINAL BONFERRONI SUMMATIONSSOBEL–UPPULURI–GALAMBOS INEQUALITIES

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 729 - 740
Copyright
Copyright © Applied Probability Trust 1996 

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References

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