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Bounds for the total variation distance between the binomial and the Poisson distribution in case of medium-sized success probabilities

Part of: Distribution theory Applications

Published online by Cambridge University Press:  14 July 2016

Michael Weba
Michael Weba*
Affiliation:
University of Applied Sciences, Fulda
*
∗Postal address: Department of Applied Computer Science, University of Applied Sciences, Fulda, Marquardstr. 35, 36039 Fulda, Germany.
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Abstract

In applied probability, the distribution of a sum of n independent Bernoulli random variables with success probabilities p1,p2,…, pn is often approximated by a Poisson distribution with parameter λ = p1 + p2 + pn. Popular bounds for the approximation error are excellent for small values, but less efficient for moderate values of p1,p2,…,pn.

Upper bounds for the total variation distance are established, improving conventional estimates if the success probabilities are of medium size. The results may be applied directly, e.g. to approximation problems in risk theory.

Keywords

Binomial distributionPoisson distributiontotal variation distancerisk theoryaccumulated claim distribution

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic) 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 97 - 104
Copyright
Copyright © Applied Probability Trust 1999 

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