Bernoulli

  • Bernoulli
  • Volume 11, Number 6 (2005), 1115-1128.

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

Adrian Röllin

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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.

Article information

Source
Bernoulli, Volume 11, Number 6 (2005), 1115-1128.

Dates
First available in Project Euclid: 16 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1137421642

Digital Object Identifier
doi:10.3150/bj/1137421642

Mathematical Reviews number (MathSciNet)
MR2189083

Zentralblatt MATH identifier
1102.60022

Keywords
Stein's method total variation metric translated Poisson distribution

Citation

Röllin, Adrian. Approximation of sums of conditionally independent variables by the translated Poisson distribution. Bernoulli 11 (2005), no. 6, 1115--1128. doi:10.3150/bj/1137421642. https://projecteuclid.org/euclid.bj/1137421642


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References

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