A note on the relationship between Spearman's rho and Kendall's iota for extreme order statistics

作者：Chen Yung Pin^*

来源：Journal of Statistical Planning and Inference, 2007, 137(7): 2165-2171.

DOI：10.1016/j.jspi.2006.07.003

• copula
• order statistic
• Spearman's rho
• kendall's iota

This note focuses on the relationship between Spearman's rho(n) and Kendall's tau(n) for the two extreme order statistics X((l)) and X((n)) of n independent and identically distributed continuous random variables. We present three new formulas for computing Spearman's rho(n). One of the formulas leads to a recursion relation. We use this recursion relation to establish inequality relationships between rho(n) and tau(n). The recursion relation also provides an alternative proof of the result that the sequence of ratios rho(n)/tau(n) converges to (3)/(2) as the sample size n goes to infinity.

• 出版日期2007-7-1