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  • Research Article
  • Open Access

Exact Kolmogorov and total variation distances between some familiar discrete distributions

Journal of Inequalities and Applications20062006:64307

  • Received: 9 June 2005
  • Accepted: 24 August 2005
  • Published:


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.


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


Authors’ Affiliations

Departamento de Métodos Estadísticos, Universidad de Zaragoza, Zaragoza, 50009, Spain


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© J. A. Adell and P. Jodrá 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.