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A refinement of multivariate Bonferroni-type inequalities

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: School of Mathematics and Statistics, F07, University of Sydney, N.S.W. 2006, Australia.
∗Postal address: School of Mathematics and Statistics, F07, University of Sydney, N.S.W. 2006, Australia.
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Abstract

Technology developed in a predecessor paper (Chen and Seneta (1996)) is applied to provide, in a unified manner, a sharpening of bivariate Bonferroni-type bounds on P(v1≥r, v2≥u) obtained by Galambos and Lee (1992; upper bound) and Chen and Seneta (1986; lower bound).

Keywords

Bivariate binomial momentsindicator functionsproduct probability spaceBonferroni inequalities

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 276 - 282
Copyright
Copyright © 2000 by The Applied Probability Trust 

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References

Chen, T. (1996). Multivariate Bonferroni-type inequalities and optimality. Ph.D. thesis, School of Mathematics and Statistics, University of Sydney.Google Scholar
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