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On Estimation of the Scale and Location Parameters of Distribution Tails

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Abstract

Estimators of the location and scale parameters are proposed for tails of distributions belonging to the Gumbel or Fréchet maximum domain of attraction using only higher order statistics of the sample. The related problem for the Gumbel domain of attraction is considered for the first time.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russia

    P. I. Akhtyamov

  2. Trapeznikov Institute of Control Sciences of RAS, 65 Profsoyuznaya St., Moscow, 117997, Russia

    I. V. Rodionov

  3. Steklov Mathematical Institute, Russian Academy of Sciences, 3 Gubkina St., Moscow, 119991, Russia

    I. V. Rodionov

Authors
  1. P. I. Akhtyamov
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  2. I. V. Rodionov
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Correspondence to P. I. Akhtyamov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 1, pp. 25–49, 2020.

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Akhtyamov, P.I., Rodionov, I.V. On Estimation of the Scale and Location Parameters of Distribution Tails. J Math Sci 262, 406–424 (2022). https://doi.org/10.1007/s10958-022-05824-w

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  • DOI: https://doi.org/10.1007/s10958-022-05824-w

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