Bernoulli

  • Bernoulli
  • Volume 6, Number 4 (2000), 581-590.

Estimating Stein's constants for compound Poisson approximation

A. D. Barbour and Aihua Xia

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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.

Article information

Source
Bernoulli, Volume 6, Number 4 (2000), 581-590.

Dates
First available in Project Euclid: 8 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081449593

Mathematical Reviews number (MathSciNet)
MR2001e:60040

Zentralblatt MATH identifier
0959.62014

Keywords
coupling immigration-death process Kolmogorov metric Stein's method

Citation

Barbour, A. D.; Xia, Aihua. Estimating Stein's constants for compound Poisson approximation. Bernoulli 6 (2000), no. 4, 581--590. https://projecteuclid.org/euclid.bj/1081449593


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References

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