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Multivariate Identities, Permutation and Bonferroni Upper Bounds

Published online by Cambridge University Press:  12 September 2008

Tuhao Chen  and
E. Seneta
Tuhao Chen
Affiliation:
School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia
E. Seneta
Affiliation:
School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia
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Abstract

We derive identities for the probability that at least a1 and at least a2, and for the probability that exactly a1 and exactly a2, out of n and N events occur (1 ≤ a1 ≤ n, 1 ≤ a2 ≤ N). From this, we produce multivariate permutation hybrid upper bounds, and a multivariate Bonferroni-type upper bound which includes Galambos and Xu's [2] optimal result. The methodology generalizes that of Hoppe and Seneta [3, §5]. A numerical example is given.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 4 , December 1995 , pp. 331 - 342
Copyright
Copyright © Cambridge University Press 1995

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References

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