Abstract
Consider independent and identically distributed random variables {Xnk, 1 ≤ k ≤ m, n ≥ 1} from the Pareto distribution. We randomly select two adjacent order statistics from each row, Xn(i) and Xn(i+1), where 1 ≤ i ≤ m − 1. Then, we test to see whether or not strong and weak laws of large numbers with nonzero limits for weighted sums of the random variables Xn(i+1)/Xn(i) exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.
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