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Approximation by Penultimate Stable Laws

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  • Laurens F.M. de Haan
  • Liang Peng

    (Erasmus University Rotterdam)

  • H. Iglesias Pereira

    (University of Lisbon)

Abstract

In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by asequence of stable distributions with indices alpha_n o 2 than by a normal distribution. We discusswhen this happens and how much the convergence rate can be improved by using penultimateapproximations. Similar results are valid for other stable distributions.

Suggested Citation

  • Laurens F.M. de Haan & Liang Peng & H. Iglesias Pereira, 1997. "Approximation by Penultimate Stable Laws," Tinbergen Institute Discussion Papers 97-100/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19970100
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    References listed on IDEAS

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    1. de Haan, L. & Pereira, T. Themido, 1999. "Estimating the index of a stable distribution," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 39-55, January.
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