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

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  • André Adler

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.

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  • André Adler, 2005. "Limit theorems for randomly selected adjacent order statistics from a Pareto distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:853426
    DOI: 10.1155/IJMMS.2005.3427
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