Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T08:50:55.301Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Agnew, R. A. (1972) Inequalities with application to economic risk analysis. J. Appl. Prob. 2, 441–444.CrossRefGoogle Scholar
[2] Ben-Tal, A. and Hochman, E. (1972) More bounds on the expectation of a convex function of a random variable. J. Appl. Prob. 4, 803–812.Google Scholar
[3] Brook, D. (1966) Bounds for moment generating functions and for extinction probabilities. J. Appl. Prob. 3, 171–178.CrossRefGoogle Scholar
[4] Hoeffding, W. (1963) Probability inequalities for sums of bounded random variables. J. Amer Statist. Assoc. 58, 13–30.CrossRefGoogle Scholar