Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 64307, 8 pages

Exact Kolmogorov and total variation distances between some familiar discrete distributions

José A. Adell and P. Jodrá

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

Received 9 June 2005; Accepted 24 August 2005

Copyright © 2006 José A. Adell and P. Jodrá. 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.


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 W function.