# A sharp uniform bound for the distribution of sums of Bernoulli trials

Jean Bernard Baillon, Roberto Cominetti, José Vaisman

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

10 Citas (Scopus)

## Resumen

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 σ n (S n = j) ≤ η, where σ n denotes the standard deviation of S n, and η is a universal constant. We compute the best possible constant η ~ 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.

Idioma original Inglés 352-361 10 Combinatorics Probability and Computing 25 3 https://doi.org/10.1017/S0963548315000127 Publicada - 1 may. 2016

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