Estimating Stein's constants for compound Poisson approximation
type: Item
instance of: scholarly article
title: Estimating Stein's constants for compound Poisson approximation
zbMATH Open document ID: 0959.62014
DOI: 10.2307/3318506
author: Aihua Xia
author: A. D. Barbour
published in: Bernoulli
publication date: 2001-05-02T00:00:00Z
review text: Stein's method for compound Poisson approximation was introduced by \textit{A.D. Barbour}, \textit{L.H.Y. Chen} and \textit{W.-L. Loh} [Ann. Probab. 20, No. 4, 1843-1866 (1992; Zbl 0765.60015)]. 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 the Poisson approximation. Here, it is shown 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.
Mathematics Subject Classification ID: 62E17
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1529274
zbMATH Keywords: Stein equation
zbMATH Keywords: Poisson approximation
zbMATH Keywords: compound Poisson distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/3318506
OpenAlex ID: W2037312113
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description: scientific article; zbMATH DE number 1529274