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dec 2005 Approximation of sums of conditionally independent variables by the translated Poisson distribution
Adrian Röllin
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Bernoulli 11(6): 1115-1128 (dec 2005). DOI: 10.3150/bj/1137421642

Abstract

It is shown that the sum of a Poisson and an independent approximately normally distributed integer-valued random variable can be well approximated in total variation by a translated Poisson distribution, and further that a mixed translated Poisson distribution is close to a mixed translated Poisson distribution with the same random shift but fixed variance. Using these two results, a general approach is then presented for the approximation of sums of integer-valued random variables, having some conditional independence structure, by a translated Poisson distribution. We illustrate the method by means of two examples. The proofs are mainly based on Stein's method for distributional approximation.

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Adrian Röllin. "Approximation of sums of conditionally independent variables by the translated Poisson distribution." Bernoulli 11 (6) 1115 - 1128, dec 2005. https://doi.org/10.3150/bj/1137421642

Information

Published: dec 2005
First available in Project Euclid: 16 January 2006

zbMATH: 1102.60022
MathSciNet: MR2189083
Digital Object Identifier: 10.3150/bj/1137421642

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

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Vol.11 • No. 6 • dec 2005
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