Exact laws for sums of ratios of order statistics from the Pareto distribution |
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| Authors: | André Adler |
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| Affiliation: | (1) Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois, 60616, USA |
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| Abstract: | 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). |
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| Keywords: | Almost sure convergence weak law of large numbers strong law of large numbers order statistics exact laws |
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