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Exact Kolmogorov and total variation distances between some familiar discrete distributions

Abstract

We give exact closed-form expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters. In the Poisson case, such expressions are related with the Lambert function.

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Correspondence to José A. Adell.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Adell, J.A., Jodrá, P. Exact Kolmogorov and total variation distances between some familiar discrete distributions. J Inequal Appl 2006, 64307 (2006). https://doi.org/10.1155/JIA/2006/64307

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  • DOI: https://doi.org/10.1155/JIA/2006/64307

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