## Toward a usable theory of Chernoff Bounds for heterogeneous and partially dependent random variables (1992)

Citations: | 6 - 1 self |

### BibTeX

@MISC{Siegel92towarda,

author = {Alan Siegel},

title = {Toward a usable theory of Chernoff Bounds for heterogeneous and partially dependent random variables},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

Let X be a sum of real valued random variables and have a bounded mean E[X]. The generic Chernoff-Hoeffding estimate for large deviations of X is: P rfX \GammaE[X ] ag min 0 e \Gamma(a+E[X]) E[e X ], which applies with a 0 to random variables with very small tails. At issue is how to use this method to attain sharp and useful estimates. We present a number of Chernoff-Hoeffding bounds for sums of random variables that may have a variety of dependent relationships and that may be heterogeneously distributed. AMS classifications 60F10, Large deviations, 68Q25 Analysis of algorithms, 62E17, Approximations to distributions (nonasymptotic), 60E15, Inequalities. Key words: Hoeffding bounds, Chernoff bounds, dependent random variables, Bernoulli trials. This research was supported, in part, by grants NSF-CCR-8902221, NSF-CCR-8906949, and NSF-CCR-9204202. 1 Summary In the analysis of probabilistic algorithms, some of the following problems may arise, possibly in complex combinations....