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Stein’s method for conditional compound Poisson approximation

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  • Gan, H.L.
  • Xia, A.

Abstract

The occurrence of rare events can often be well described by a compound Poisson distribution. However, one can only start modelling the occurrence of rare events after such events have happened, thus a conditional compound Poisson distribution is more appropriate in applications. In this note, we develop Stein’s method for conditional compound Poisson approximation. Several applications are given to demonstrate the advantage of the direct approach of Stein’s method.

Suggested Citation

  • Gan, H.L. & Xia, A., 2015. "Stein’s method for conditional compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 19-26.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:19-26
    DOI: 10.1016/j.spl.2015.01.033
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    References listed on IDEAS

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    1. Barbour, A. D. & Utev, Sergey, 1999. "Compound Poisson approximation in total variation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 89-125, July.
    2. Novak, S.Y. & Xia, A., 2012. "On exceedances of high levels," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 582-599.
    3. Michel, R., 1987. "An Improved Error Bound for the Compound Poisson Approximation of a Nearly Homogeneous Portfolio," ASTIN Bulletin, Cambridge University Press, vol. 17(2), pages 165-169, November.
    4. 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.
    5. Novak, S. Y., 2003. "On the accuracy of multivariate compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 35-43, March.
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