Electronic Communications in Probability

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

Fraser Daly

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1511427622

Digital Object Identifier
doi:10.1214/17-ECP101

Mathematical Reviews number (MathSciNet)
MR3734106

Zentralblatt MATH identifier
06827049

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

Keywords
compound Poisson approximation Stein’s method Kolmogorov distance runs reliability

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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References

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