## Bernoulli

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

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

#### 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

https://projecteuclid.org/euclid.bj/1137421642

Digital Object Identifier
doi:10.3150/bj/1137421642

Mathematical Reviews number (MathSciNet)
MR2189083

Zentralblatt MATH identifier
1102.60022

#### 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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