次序统计量和的渐近分布（Ⅱ）

The Asymptotic Distributions for Sums ofOrder Statistics (Ⅱ )￣1)CHENG Shihong

设是独立同分布随机变量列，是Ｘ＿１，…，Ｘ＿ｎ的次序统计量。对非负实数ｐ＿ｎ，ｑ＿ｎ和满足的整数ｌ＿ｎ，ｒ＿ｎ，令当满足ｌ＿ｎ≡ｌ（ｌ是一给定的正整数）或ｌ＿ｎ→但ｌ＿ｎ／（ｎ＋１）→０，同时满足ｎ──ｒ＿ｎ＋１→∞但ｒ＿ｎ／（ｎ＋１）→λ∈（０，１］时，我们讨论了标准化后之和以的渐近分布问题。关于截断和及修正截断和的结果将作为特例给出。特别地，我们改进了格里芬关于修正截断和渐近正态性的结论；对于他的一个猜测也作出了正面的回答。

et be a sequence of i. i. d. random variables with a common nondegenerated. f. , for each , denote as the order statistics of X_1 , ... ,X_n and for integers and nonnegative real numbers p_n and q_n , define Assume that satisfies either l_n=l for all (l is a fixed positive integer) , orl_n→∞ and l_n/(n+1)→0 and that satisfies n─r_n+ 1→∞ and Wewill discuss asymptotic distributions of normalized sums . Results ontrimmed sums and winsorized sums will be obtained as special cases of the above sums. Especial-ly,we will improve a Griffin's result on asymptotic normality of winsorized sums and give a posi-tive reply for one of his conjectures.