The extreme gap in the multivariate Poisson process

B. Kopociński

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We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall. It is shown, among other results, that if p₁ = P (X₁=1), ..., p_n = P (X_n=1) satisfy some appropriate...