Electronic Communications in Probability

On magic factors in Stein’s method for compound Poisson approximation

Fraser Daly

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One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable. To illustrate the advantages offered by these new bounds, we consider applications to runs, reliability systems, Poisson mixtures and sums of independent random variables.

Article information

Electron. Commun. Probab., Volume 22 (2017), paper no. 67, 10 pp.

Received: 29 June 2017
Accepted: 13 November 2017
First available in Project Euclid: 23 November 2017

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Zentralblatt MATH identifier

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems 62E10: Characterization and structure theory

compound Poisson approximation Stein’s method Kolmogorov distance runs reliability

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Daly, Fraser. On magic factors in Stein’s method for compound Poisson approximation. Electron. Commun. Probab. 22 (2017), paper no. 67, 10 pp. doi:10.1214/17-ECP101. https://projecteuclid.org/euclid.ecp/1511427622

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