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

Przemysław Matuła and André Adler

Statistics & Probability Letters, 2022, vol. 182, issue C

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.

Keywords: Strong law of large numbers; Weighted sums; i.i.d. random variables; Order statistics; Range; Pareto distribution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109297

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