In probability theory, Bennett's inequality provides an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount. Bennett's inequality was proved by George Bennett of the University of New South Wales in 1962.
Then for any t ≥ 0,
where h(u) = (1 + u)log(1 + u) – u.
- Bernstein inequalities (probability theory)
- Hoeffding's inequality
- Azuma's inequality
- McDiarmid's inequality
- Markov inequality
- Chebyshev's inequality
- Bennett, G. (1962). "Probability Inequalities for the Sum of Independent Random Variables". Journal of the American Statistical Association 57 (297): 33–45. doi:10.2307/2282438.
- Devroye, Luc; Lugosi, Gábor (2001). Combinatorial methods in density estimation. Springer. p. 11. ISBN 978-0-387-95117-1.
- Freedman, D. A. (1975). On tail probabilities for martingales. 3. The Annals of Probability. pp. 100–118.
- Fan, X.; Grama, I.; Liu, Q. (2012). Hoeffding's inequality for supermartingales 122. Stochastic Processes and their Applications. pp. 3545–3559. doi:10.1016/j.spa.2012.06.009.
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