Abstract
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and Rényi/relative Tsallis distances (including Pearson’s _2). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions.
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Dedicated to Professor Vygantas Paulauskas on the occasion of his 75th birthday
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Research was partially supported by the Simons Foundation and the NSF grant DMS-1855575.
Research was partially supported by SFB 1283.
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Bobkov, S.G., Chistyakov, G.P. & Götze, F. Nonuniform bounds in the Poisson approximation with applications to informational distances. II. Lith Math J 59, 469–497 (2019). https://doi.org/10.1007/s10986-019-09468-3
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DOI: https://doi.org/10.1007/s10986-019-09468-3