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- W1554953295 abstract "In this note we establish a uniform bound for the distribution of a sum $S_n=X_1+cdots+X_n$ of independent non-homogeneous Bernoulli trials. Specifically, we prove that $sigma_n mathbb{P}(S_n!=!j)leqeta$ where $sigma_n$ denotes the standard deviation of $S_n$ and $eta$ is a universal constant. We compute the best possible constant $etasim 0.4688$ 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." @default.
- W1554953295 created "2016-06-24" @default.
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- W1554953295 date "2008-06-13" @default.
- W1554953295 modified "2023-09-27" @default.
- W1554953295 title "A sharp uniform bound for the distribution of a sum of Bernoulli random variables" @default.
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