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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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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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Keywords

  • Total Variation
  • Binomial Distribution
  • Variation Distance
  • Negative Binomial Distribution
  • Discrete Distribution
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