On Large Deviations for Sums of i.i.d. Bernoulli Random Variables

On Large Deviations for Sums of i.i.d. Bernoulli Random Variables

Tail probabilities are studied for the binomial distribution. The Hoeffding inequality is sharpened in this particular case through estimating an integral factor in the Esscher transform, which is omitted in Hoeffding’s proof. This approach was already used by Talagrand (1995) in the general case. H...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-11, Vol.234 (6), p.816-828
Hauptverfasser: Nagaev, S. V., Chebotarev, V. I.
Format: Artikel
Sprache:eng
Schlagworte:
Binomial distribution
DISTRIBUTION
INTEGRALS
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
PROBABILITY
Random variables
RANDOMNESS
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Zusammenfassung:Tail probabilities are studied for the binomial distribution. The Hoeffding inequality is sharpened in this particular case through estimating an integral factor in the Esscher transform, which is omitted in Hoeffding’s proof. This approach was already used by Talagrand (1995) in the general case. However, our results are much more precise. In particular, all involved constants are given in the explicit form.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-4049-9