Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).
@article{bwmeta1.element.doi-10_1007_s11533-005-0001-6,
author = {Andr\'e Adler},
title = {Exact laws for sums of ratios of order statistics from the Pareto distribution},
journal = {Open Mathematics},
volume = {4},
year = {2006},
pages = {1-4},
zbl = {1097.62008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0001-6}
}
André Adler. Exact laws for sums of ratios of order statistics from the Pareto distribution. Open Mathematics, Tome 4 (2006) pp. 1-4. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0001-6/
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