International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3427-3441
doi:10.1155/IJMMS.2005.3427
Limit theorems for randomly selected adjacent order statistics from a Pareto distribution
Department Applied of Mathematics, College of Science and Letters, Illinois Institute of Technology, Chicago 60616, IL, USA
Received 28 May 2005; Revised 23 September 2005
Copyright © 2005 André Adler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Consider independent and identically distributed random variables
{Xnk, 1≤k≤m, n≥1} from the Pareto distribution. We randomly select two adjacent order statistics from each row, Xn(i) and Xn(i+1), where 1≤i≤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
Xn(i+1)/Xn(i) exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.