Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 965712, 13 pages
doi:10.1155/2009/965712
Research Article

The Kolmogorov Distance between the Binomial and Poisson Laws: Efficient Algorithms and Sharp Estimates

José A. Adell, José M. Anoz, and Alberto Lekuona

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

Received 21 May 2009; Accepted 9 October 2009

Academic Editor: Andrei Volodin

Copyright © 2009 José A. Adell et al. 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.

Abstract

We give efficient algorithms, as well as sharp estimates, to compute the Kolmogorov distance between the binomial and Poisson laws with the same mean λ. Such a distance is eventually attained at the integer part of λ+1/2−λ+1/4. The exact Kolmogorov distance for λ≤2−2 is also provided. The preceding results are obtained as a concrete application of a general method involving a differential calculus for linear operators represented by stochastic processes.