李永明,杨善朝.NA序列下经验分布函数的渐近正态性及其应用[J].数学研究及应用,2006,26(3):457~464
NA序列下经验分布函数的渐近正态性及其应用
Asymptotic Normality of the Empirical Distribution under Negatively Associated Sequences and its Applications
投稿时间:2003-10-30  
DOI:10.3770/j.issn:1000-341X.2006.03.005
中文关键词:  NA列  经验分布函数  渐近正态性  生存函数.
英文关键词:NA sequences  empirical distribution  survival function  asymptotic normality.
基金项目:the National Natural Science Foundation of China (10161004), the Natural Science Foundation of Jiangxi (0611068) and Science Foundation of Shangrao Normal College.
作者单位
李永明 上饶师范学院数学系, 江西 上饶 334001 
杨善朝 广西师范大学数学系, 广西 桂林 541004 
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中文摘要:
      本文在NA负相协序列下利用熟知的相依情形的大小块分割的方法,建立了经验分布函数的渐近正态性.作为在可靠性中的应用,得到了生存函数$\overline F(x)=P(X>x)$估计的渐近正态性.
英文摘要:
      By the well-known large and small blocks parting method for dependent situations, we establish the asymptotic normality of the Empirical Distribution Function under Negatively Associated Sequences. As its application in reliablity problems, a natural estimate $\overline F_n(x) $ for the survival function $\overline F(x)=P(X>x)$ is proposed, and the asymptotic normality of $n^{\frac{1}{2}}[ \overline F_{n}(x)- \overline F (x)]$ is established.
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