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Some remarks on probability inequalities for sums of bounded convex random variables

Published online by Cambridge University Press:  14 July 2016

M. Goldstein
M. Goldstein*
Affiliation:
Polytechnic Institute of New York∗
*
∗Now at Baruch College, City University of New York.
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Abstract

Let X1, X2, · ··, Xn be independent random variables such that ai ≦ Xi ≦ bi, i = 1,2,…n. A class of upper bounds on the probability P(S−ES ≧ nδ) is derived where S = Σf(Xi), δ > 0 and f is a continuous convex function. Conditions for the exponential convergence of the bounds are discussed.

Keywords

CONVEXBOUNDED RANDOM VARIABLEPROBABILITY BOUNDS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 155 - 158
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Agnew, R. A. (1972) Inequalities with application to economic risk analysis. J. Appl. Prob. 2, 441–444.CrossRefGoogle Scholar
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