Limit theorems for randomly selected adjacent order statistics from a Pareto distribution

摘要

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.