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
André Adler
Department Applied of Mathematics, College of Science and Letters, Illinois Institute of Technology, Chicago 60616, IL, USA
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.