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Generalized Bonferroni inequalities

Part of: Combinatorial probability Limit theorems

Published online by Cambridge University Press:  14 July 2016

Thomas H. Spencer
Thomas H. Spencer*
Affiliation:
University of Nebraska at Omaha
*
∗ Postal address: Department of Mathematics and Computer Science, University of Nebraska at Omaha, Omaha, NE 68182, USA. Email address: spencer@unocss.unomaha.edu
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Abstract

Consider a number of events in a probability space. Let X be a random variable that is the number of events that occur. Given some of the moments of the distribution of X, it is possible to obtain bounds on the probability that at least one event occurs. The best possible bounds are given here. If there are many equiprobable events that are d- wise independent, and d is even, then the probability that at least one event happens is at least 1 — O(µ–d/2), where μ = E(X).

Keywords

BOUNDSOCCURRENCE OF INDEPENDENT EVENTSESCAPE PROBABILITY

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 409 - 417
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Supported in part by the National Science Foundation under grants CCR-8810609 and CDA-8805910 and by the University Committee on Research, University of Nebraska at Omaha.

Much of the work for this paper was done while the author was at the Computer Science Department, Rensselaer Polytechnic Institute, Troy, NY 12180.

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