Limit theorems for randomly selected adjacent order statistics from a Pareto distribution

André Adler

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-15

Abstract:

Consider independent and identically distributed random variables { X n k , 1 ≤ k ≤ m , n ≥ 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 ≤ 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 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:853426

DOI: 10.1155/IJMMS.2005.3427

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