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Estimating Stein's constants for compound Poisson approximation


Barbour, A D; Xia, A (2000). Estimating Stein's constants for compound Poisson approximation. Bernoulli, 6(4):581-590.

Abstract

Stein's method for compound Poisson approximation was introduced by Barbour, Chen and Loh. One difficulty in applying the method is that the bounds on the solutions of the Stein equation are by no means as good as for Poisson approximation. We show that, for the Kolmogorov metric and under a condition on the parameters of the approximating compound Poisson distribution, bounds comparable with those obtained for the Poisson distribution can be recovered.

Abstract

Stein's method for compound Poisson approximation was introduced by Barbour, Chen and Loh. One difficulty in applying the method is that the bounds on the solutions of the Stein equation are by no means as good as for Poisson approximation. We show that, for the Kolmogorov metric and under a condition on the parameters of the approximating compound Poisson distribution, bounds comparable with those obtained for the Poisson distribution can be recovered.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:coupling; immigration-death process; Kolmogorov metric; Stein's method
Language:English
Date:2000
Deposited On:07 Apr 2010 13:13
Last Modified:05 Apr 2016 13:25
Publisher:Bernoulli Society for Mathematical Statistics and Probability
ISSN:1350-7265
Publisher DOI:https://doi.org/10.2307/3318506
Official URL:http://projecteuclid.org/euclid.bj/1081449593

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