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

✍ Scribed by André Adler

• Book ID: 107385631
• Publisher: SP Versita
• Year: 2006
• Tongue: English
• Weight: 120 KB
• Volume: 4
• Category: Article
• ISSN: 1895-1074
• DOI: 10.1007/s11533-005-0001-6

✦ Synopsis

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).