Acta Scientiarum Naturalium Universitatis Pekinensis

Previous Articles     Next Articles

Central Limit Theorem for Sums of Order Statistics

YANG Jingping   

  1. Department of Probability and Statistics, Peking University, 100871, e-mail: yang
  • Received:1994-02-23 Online:1995-09-20 Published:1995-09-20



  1. 北京大学概率系,北京,100871

Abstract: Let {X, Xi, i≥1} be i.i.d. random variables with non-degenerate d.f.F, and |X(1)n|≥|X(2)n|≥...≥|X(n)n| be the order statistics of |X1|, |X2|,...,|Xn|. For rn→+∞,and rn/n→0 as n→+∞, write (rn)Sn=∑ni=rn+1X(i)n. This article gets the sufficient and necessary condition for (rn)Sn convcrgcs to normal in distribution.

Key words: trimmed sum, order statistics

摘要: 设{X, Xi, i≥1} 为独立同分布随机变量列,具有共同的非退化分布函数,并且|X(1)n|≥|X(2)n|≥...≥|X(n)n|为|X1|, |X2|,...,|Xn|的次序统计量。对于rn→+∞,rn/n→0,记(rn)Sn=∑ni=rn+1X(i)n。本文得到了依分布收敛到正态的充要条件。

关键词: 次序统计量, 截断和

CLC Number: