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)andXn(i+1), where1≤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 variablesXn(i+1)/Xn(i)exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.