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Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 64307, 8 pages
doi:10.1155/JIA/2006/64307

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

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 W function.