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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 ,
Meena Pradhan  and
S. P. Shah
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.
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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.

Keywords

BEST LINEAR BOUNDSBINOMIAL MOMENTSPROBABILITY OF OCCURRENCE OF AT LEAST m OUT OF n EVENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1127 - 1132
Copyright
Copyright © Applied Probability Trust 

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References

Dawson, D. A. and Sankoff, D. (1967) An inequality for probabilities. Proc. Amer. Math. Soc. 18, 504–507.CrossRefGoogle Scholar
Galambos, J. (1977) Bonferroni inequalities. Ann. Prob. 4, 577–581.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