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Probability Inequalities for Sums of Bounded Random Variables
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 Pr {S – 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.
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Metadata
- Authors
- Hoeffding, W.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1963-03
- Volume
- 58
- Issue
- 301
- Pages
- 13-30
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W4233413206
- Cited by
- 4,852
- References
- 1
- FWCI
- 3.01
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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