# Exact laws for sums of ratios of order statistics from the Pareto distribution

Open Mathematics (2006)

• Volume: 4, Issue: 1, page 1-4
• ISSN: 2391-5455

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## Abstract

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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).

## How to cite

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André Adler. "Exact laws for sums of ratios of order statistics from the Pareto distribution." Open Mathematics 4.1 (2006): 1-4. <http://eudml.org/doc/268739>.

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).},
journal = {Open Mathematics},
keywords = {60F05; 60F15},
language = {eng},
number = {1},
pages = {1-4},
title = {Exact laws for sums of ratios of order statistics from the Pareto distribution},
url = {http://eudml.org/doc/268739},
volume = {4},
year = {2006},
}

TY - JOUR
TI - Exact laws for sums of ratios of order statistics from the Pareto distribution
JO - Open Mathematics
PY - 2006
VL - 4
IS - 1
SP - 1
EP - 4
AB - 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).
LA - eng
KW - 60F05; 60F15
UR - http://eudml.org/doc/268739
ER -

## References

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1. [1] A. Adler: “Exact Strong Laws”, Bulletin Institute Mathematics Academia Sinica, Vol. 28(3), (2000), pp. 141–166. Zbl0966.60024
2. [2] A. Adler: “Exact Laws for Sums of Order Statistics from the Pareto Distrbution”, Bulletin Institute Mathematics Academia Sinica, Vol. 31(3), (2003), pp. 181–193.
3. [3] W. Feller: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed., John Wiley, New York, 1968.
4. [4] M. Klass and H. Teicher: “Iterated Logarithm Laws for Asymmetric Random Variables Barely With or Without Finite Mean”, Annals Probab., Vol. 5(6), (1977), pp. 861–874. Zbl0372.60042

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