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Comparison between the rates of convergence of extremes under linear and under power normalization

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Abstract

By using the theory of the second-order regular variation, we study the rates of the weak convergence of the maximum order statistics under power normalization. The exact rates are obtained in the uniform metric and the total variation metric. The relationship between the rates of convergence under linear and under power normalization is derived. Some illustrative examples are given for comparing the rates of convergence.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    H. M. Barakat & E. M. Nigm

  2. Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt

    Magdy E. El-Adll

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  1. H. M. Barakat
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  2. E. M. Nigm
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  3. Magdy E. El-Adll
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Correspondence to Magdy E. El-Adll.

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Barakat, H.M., Nigm, E.M. & El-Adll, M.E. Comparison between the rates of convergence of extremes under linear and under power normalization. Stat Papers 51, 149–164 (2010). https://doi.org/10.1007/s00362-008-0128-1

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  • DOI: https://doi.org/10.1007/s00362-008-0128-1

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