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March 2011 Unusual strong laws for arrays of ratios of order statistics
André Adler
Braz. J. Probab. Stat. 25(1): 34-43 (March 2011). DOI: 10.1214/09-BJPS024

Abstract

Let {Xn, k, 1 ≤ kmn, n ≥ 1} be independent random variables from the Pareto distribution. Let Xn(k) be the kth largest order statistic from the nth row of our array, where Xn(1) denotes the largest order statistic from the nth row. Then set Rn, in, jn = Xn(jn) / Xn(in) where jn < in. This paper establishes limit theorems involving weighted sums from the sequence {Rn, in, jn, n ≥ 1}, where for the first time we allow jn → ∞, but only at a slow rate.

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André Adler. "Unusual strong laws for arrays of ratios of order statistics." Braz. J. Probab. Stat. 25 (1) 34 - 43, March 2011. https://doi.org/10.1214/09-BJPS024

Information

Published: March 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1298.60038
MathSciNet: MR2746491
Digital Object Identifier: 10.1214/09-BJPS024

Keywords: Almost sure convergence , Strong law of large numbers

Rights: Copyright © 2011 Brazilian Statistical Association

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Vol.25 • No. 1 • March 2011
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