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Zbl 1087.60020
Adler, André
Limit theorems for randomly selected adjacent order statistics from a Pareto distribution. (English)
[J] Int. J. Math. Math. Sci. 2005, No. 21, 3427-3441 (2005). ISSN 0161-1712; ISSN 1687-0425/e

Summary: Consider independent and identically distributed random variables $\{X_{nk},\ 1\le k\le m, n \ge 1\}$ from the Pareto distribution. We randomly select two adjacent order statistics from each row, $X_{n(i)}$ and $X_{n(i+1)}$, where $1\le i \le m-1$. Then, we test to see whether or not strong and weak laws of large numbers with nonzero limits for weighted sums of the random variables $X_{n(i+1)}/X_{n(i)}$ exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.

MSC 2000:: *60F05 Weak limit theorems

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Zentralblatt MATH Berlin [Germany]