A Sharp Uniform Bound for the Distribution of Sums of Bernoulli Trials
Author
dc.contributor.author
Baillon, Jean-Bernard
Author
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Cominetti Cotti-Cometti, Roberto
Author
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Vaisman Romero, José
Admission date
dc.date.accessioned
2016-07-05T21:21:27Z
Available date
dc.date.available
2016-07-05T21:21:27Z
Publication date
dc.date.issued
2016
Cita de ítem
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Combinatorics, Probability and Computing (2016) 25, 352–361.
en_US
Identifier
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doi:10.1017/S0963548315000127
Identifier
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https://repositorio.uchile.cl/handle/2250/139427
General note
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Artículo de publicación ISI
en_US
Abstract
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In this note we establish a uniform bound for the distribution of a sum S-n = X-1 + ... + X-n of independent non-homogeneous Bernoulli trials. Specifically, we prove that sigma P-n(S-n = j) <= eta, where sigma(n) denotes the standard deviation of S-n, and eta is a universal constant. We compute the best possible constant eta similar to 0.4688 and we show that the bound also holds for limits of sums and differences of Bernoullis, including the Poisson laws which constitute the worst case and attain the bound. We also investigate the optimal bounds for n and j fixed. An application to estimate the rate of convergence of Mann's fixed-point iterations is presented.
en_US
Patrocinador
dc.description.sponsorship
Nucleo Milenio Informacion y Coordinacion en Redes
ICM/FIC P10-024F
FONDECYT
1130564
1100046