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Inequalities for the probability of the occurrence of at least m out of n events

Published online by Cambridge University Press:  14 July 2016

Y. S. Sathe*
Affiliation:
University of Bombay
Meena Pradhan*
Affiliation:
University of Bombay
S. P. Shah*
Affiliation:
University of Bombay
*
Postal address: Department of Statistics, University of Bombay, University Campus, Bombay 400 098, India.
Postal address: Department of Statistics, University of Bombay, University Campus, Bombay 400 098, India.
Postal address: Department of Statistics, University of Bombay, University Campus, Bombay 400 098, India.

Abstract

Given n events A1, A2, · ··, An, bounds are obtained for the probability of the occurrence of at least m out of the n events. The bounds are linear in terms of S1 and S2 where S1 = Σi P(Ai) and S2 = Σi<jΡ (Α i,Α j). The bounds are illustrated with an example. For m = 1 the bounds are the same as the best known linear bounds in terms of S1 and S2.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 

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References

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