Limit theorems for randomly selected adjacent order statistics from a Pareto distribution. (English) Zbl 1087.60020

Summary: Consider independent and identically distributed random variables \(\{X_{nk},\;1\leq k\leq m, n \geq 1\}\) from the Pareto distribution. We randomly select two adjacent order statistics from each row, \(X_{n(i)}\) and \(X_{n(i+1)}\), where \(1\leq i \leq m-1\). 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 \(X_{n(i+1)}/X_{n(i)}\) exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.


60F05 Central limit and other weak theorems
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