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Most stringent bounds on the probability of the union and intersection of m events for systems partially specified by s1, s2, …sk, 2 ≦ k < m

Published online by Cambridge University Press:  14 July 2016

Seymour M. Kwerel
Seymour M. Kwerel*
Affiliation:
Baruch College, City University of New York
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Abstract

For dependent probability systems of m events partially specified by the quantities Sv, the sum of the probabilities of each of the combinations of v events, v = 1, 2, …, 2 ≦ k < m; this paper develops the most stringent upper and lower bounds on P1, the probability of the union of the m events; and on P[m], the probability of the simultaneous occurrence of the m events.

Keywords

PARTIALLY SPECIFIED DEPENDENT SYSTEMSMOST STRINGENT BOUNDS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 612 - 619
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Galambos, J. (1973) A general Poisson limit theorem of probability theory. Duke Math. J. 40, 581–586.Google Scholar
[2] Hadley, G. (1962) Linear Programming. Addison-Wesley, Palo Alto, California.Google Scholar
[3] Kwerel, S. M. (1968) Information retrieval for media planning. Management Sci. 15, 137–169.Google Scholar
[4] Kwerel, S. M. (1975) Most stringent bounds on aggregated probabilities of partially specified dependent probability systems. J. Amer. Statist. Assoc. 70 To appear.Google Scholar
[5] Kwerel, S. M. (1975) Bounds on the probability of the union and intersection of m events. Adv. Appl. Prob. 7, 431–448.CrossRefGoogle Scholar
[6] Sobel, M. and Uppuluri, V. R. R. (1972) On Bonferroni-type inequalities of the same degree for the probability of unions and intersections. Ann. Math. Statist. 43, 1549–1558.CrossRefGoogle Scholar