Abstract: Let {X, X_i, 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|,...，|X_n|. For r_n→+∞，and r_n/n→0 as n→+∞, write ^(r_n)S_n=∑ⁿ_i=rn+1X⁽ⁱ⁾_n. This article gets the sufficient and necessary condition for ^(r_n)S_n convcrgcs to normal in distribution.

Key words: trimmed sum, order statistics

摘要： 设{X, X_i, 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Ｆ，并且|X⁽¹⁾_n|≥|X⁽²⁾_n|≥...≥|X⁽ⁿ⁾_n|为|X₁|, |X₂|,...，|X_n|的次序统计量。对于r_n→+∞，r_n/n→0，记^(r_n)S_n=∑ⁿ_i=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