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Exact values and sharp estimates for the total variation distance between binomial and Poisson distributions

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

José A. Adell ,
José M. Anoz  and
Alberto Lekuona
José A. Adell*
Affiliation:
Universidad de Zaragoza
José M. Anoz*
Affiliation:
Universidad de Zaragoza
Alberto Lekuona*
Affiliation:
Universidad de Zaragoza
*
∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
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Abstract

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We present a method to obtain both exact values and sharp estimates for the total variation distance between binomial and Poisson distributions with the same mean λ. We give a simple efficient algorithm, whose complexity order is to compute exact values. Such an algorithm can be further simplified for moderate sample sizes n, provided that λ is neither close to from the left nor close to from the right. Sharp estimates, better than other known estimates in the literature, are also provided. The 0s of the second Krawtchouk and Charlier polynomials play a fundamental role.

Keywords

Poisson approximationbinomial distributiontotal variation distanceKrawtchouk polynomialCharlier polynomial

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60E15: Inequalities; stochastic orderings
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 4 , December 2008 , pp. 1033 - 1047
Copyright
Copyright © Applied Probability Trust 2008 

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