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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
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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