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

• Autorzy: André Adler
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Almost sure convergence; weak law of large numbers; strong law of large numbers; order statistics; exact laws; 60F05; 60F15

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 1
• Strony: 1-4

Daty

wydano

2006-03-01

online

2006-03-01

Twórcy

autor

André Adler

• Illinois Institute of Technology

Bibliografia

• [1] A. Adler: “Exact Strong Laws”, Bulletin Institute Mathematics Academia Sinica, Vol. 28(3), (2000), pp. 141–166.
• [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.

Identyfikatory

DOI

10.1007/s11533-005-0001-6