Open Access
2017 On magic factors in Stein’s method for compound Poisson approximation
Fraser Daly
Electron. Commun. Probab. 22: 1-10 (2017). DOI: 10.1214/17-ECP101


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.


Download Citation

Fraser Daly. "On magic factors in Stein’s method for compound Poisson approximation." Electron. Commun. Probab. 22 1 - 10, 2017.


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

zbMATH: 06827049
MathSciNet: MR3734106
Digital Object Identifier: 10.1214/17-ECP101

Primary: 62E17
Secondary: 60F05 , 62E10

Keywords: compound Poisson approximation , Kolmogorov distance , reliability , Runs , Stein’s method

Back to Top