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On Stein-Chen factors for Poisson approximation

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  • Brown, Timothy C.
  • Xia, Aihua

Abstract

The Stein-Chen method for the estimation of upper bounds of the distance of the whole distribution of a point process from that of a Poisson process was investigated in Barbour and Brown (1992). A feature of the Stein-Chen approximation for random variables is the existence of "magic" factors which decrease with the mean of the Poisson distribution. Using a Wasserstein metric for process approximation, one of these factors behaves in a similar way to that for random variables but the other involves an additional logarithm. Counterexamples are presented here to show that the logarithmic factor is necessary.

Suggested Citation

  • Brown, Timothy C. & Xia, Aihua, 1995. "On Stein-Chen factors for Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 327-332, June.
    • Handle: RePEc:eee:stapro:v:23:y:1995:i:4:p:327-332
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    References listed on IDEAS

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    1. Barbour, A. D. & Brown, T. C., 1992. "Stein's method and point process approximation," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 9-31, November.
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    Cited by:

    1. Brown, Timothy C. & Weinberg, Graham V. & Xia, Aihua, 2000. "Removing logarithms from Poisson process error bounds," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 149-165, May.

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