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A sharp upper probability bound for the occurrence of at least m out of n events

Published online by Cambridge University Press:  14 July 2016

Ole Platz
Ole Platz*
Affiliation:
Risø National Laboratory
*
∗ Postal address: Risø National Laboratory, Postbox 49, DK-4000 Roskilde, Denmark.
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Abstract

Consider a fixed set of n events. Let S1 denote the sum of the probabilities of occurrence of each event and S2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S1 and S2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).

Keywords

LINEAR PROGRAMMINGDUALITY THEOREMPARTIALLY SPECIFIED SYSTEMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 978 - 981
Copyright
Copyright © Applied Probability Trust 1985 

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References

Hadley, G. (1962) Linear Programming. Addison-Wesley, Reading. Ma.Google Scholar
Kwerel, S. M. (1975) Most stringent bounds on aggregated probabilities of partially specified dependent probability systems. J. Amer. Statist. Assoc. 70, 472–479.CrossRefGoogle Scholar
Sathe, Y. S., Pradhan, M. and Shah, S. P. (1980) Inequalities for the probability of the occurrence of at least m out of n events. J. Appl. Prob. 17, 1127–1132.Google Scholar