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A note on exact laws of large numbers for the range of a sample from Pareto-type distributions

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  • Matuła, Przemysław
  • Adler, André

Abstract

We consider a triangular array of i.i.d. random variables which are positive and have a Pareto-type distribution. Denote by Rn the range in the nth row i.e. the difference between the maximal and minimal order statistics in this row. We prove the strong law of large numbers for weighted sums of (Rn)n∈N. The obtained theorem extends and generalizes some of the results known so far for Pareto distributions and arrays with fixed or logarithmically growing length of the rows.

Suggested Citation

  • Matuła, Przemysław & Adler, André, 2022. "A note on exact laws of large numbers for the range of a sample from Pareto-type distributions," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002595
    DOI: 10.1016/j.spl.2021.109297
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    References listed on IDEAS

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    1. Przemysław Matuła & André Adler & Paweł Kurasiński, 2020. "On exact strong laws of large numbers for ratios of random variables and their applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(13), pages 3153-3167, July.
    2. Matuła, Przemysław & Kurasiński, Paweł & Adler, André, 2019. "Exact strong laws of large numbers for ratios of the smallest order statistics," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 69-73.
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