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Approximation of sums of conditionally independent variables by the translated Poisson distribution


Röllin, A (2005). Approximation of sums of conditionally independent variables by the translated Poisson distribution. Bernoulli, 11(6):1115-1128.

Abstract

It is shown that the distribution of the sum of a Poisson random variable 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.

Abstract

It is shown that the distribution of the sum of a Poisson random variable 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Stein's method; total variation metric; translated Poisson distribution
Language:English
Date:2005
Deposited On:29 Nov 2010 16:26
Last Modified:06 Dec 2017 20:47
Publisher:Bernoulli Society for Mathematical Statistics and Probability
ISSN:1350-7265
Publisher DOI:https://doi.org/10.3150/bj/1137421642
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2189083
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1102.60022

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