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On exceedances of high levels

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  • Novak, S.Y.
  • Xia, A.

Abstract

The distribution of the excess process describing heights of extreme values can be approximated by the distribution of a Poisson cluster process. An estimate of the accuracy of such an approximation has been derived in [4] in terms of the Wasserstein distance. The paper presents a sharper estimate established in terms of the stronger total variation distance. We derive also a new bound to the accuracy of negative Binomial approximation to the distribution of the number of exceedances.

Suggested Citation

  • Novak, S.Y. & Xia, A., 2012. "On exceedances of high levels," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 582-599.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:582-599 DOI: 10.1016/j.spa.2011.09.003
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    References listed on IDEAS

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    1. Novak, S. Y., 2002. "Multilevel clustering of extremes," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 59-75, January.
    2. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    3. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    4. Novak, S. Y., 2003. "On the accuracy of multivariate compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 35-43, March.
    5. Michel, R., 1987. "An Improved Error Bound for the Compound Poisson Approximation of a Nearly Homogeneous Portfolio," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 17(02), pages 165-169, November.
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    Cited by:

    1. Gan, H.L. & Xia, A., 2015. "Stein’s method for conditional compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 19-26.

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