# 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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topAndré 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>.

@article{AndréAdler2006,

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).},

author = {André Adler},

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

AU - André Adler

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

top- [1] A. Adler: “Exact Strong Laws”, Bulletin Institute Mathematics Academia Sinica, Vol. 28(3), (2000), pp. 141–166. Zbl0966.60024
- [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] W. Feller: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed., John Wiley, New York, 1968.
- [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