An Inequality for Large Deviation Probabilities of Sums of Bounded i.i.d. Random Variables |
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Authors: | Bentkus V |
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Institution: | (1) Vilnius Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania |
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Abstract: | We provide precise bounds for tail probabilities, say {M
n
x}, of sums M
n
of bounded i.i.d. random variables. The bounds are expressed through tail probabilities of sums of i.i.d. Bernoulli random variables. In other words, we show that the tails are sub-Bernoullian. Sub-Bernoullian tails are dominated by Gaussian tails. Possible extensions of the methods are discussed. |
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Keywords: | probabilities of large deviations bounds for tail probabilities inequalities bounds bounded random variables |
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