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.
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