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On Tests to Distinguish Distribution Tails Invariant with Respect to the Scale Parameter

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Abstract

We propose two tests to distinguish between separable classes of distribution tails, the first of which is invariant with respect to the scale parameter and the second is invariant with respect to both location and scale parameters. The asymptotic properties of the proposed tests are established. The distributions are not assumed to belong to any maximum domain of attraction.

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Funding

The research presented in Subsection 2.1 was performed by I.V. Rodionov at the Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences and was supported by the Russian Science Foundation, project no. 21-71-00035.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    E. O. Kantonistova

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    I. V. Rodionov

Authors
  1. E. O. Kantonistova
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  2. I. V. Rodionov
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Corresponding authors

Correspondence to E. O. Kantonistova or I. V. Rodionov.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Kantonistova, E.O., Rodionov, I.V. On Tests to Distinguish Distribution Tails Invariant with Respect to the Scale Parameter. Dokl. Math. 105, 97–101 (2022). https://doi.org/10.1134/S1064562422020119

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