Abstract
Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for PrS — ES≥nt depend only on the endpoints of the ranges of the summands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.
This research was supported by the Air Force Office of Scientific Research.
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© 1994 Springer Science+Business Media New York
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Hoeffding, W. (1994). Probability Inequalities for sums of Bounded Random Variables. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_26
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DOI: https://doi.org/10.1007/978-1-4612-0865-5_26
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