| Asymptotic Normality of the Empirical Distribution under Negatively Associated Sequences and its Applications |
| Received:October 30, 2003 |
| Key Words:
NA sequences empirical distribution survival function asymptotic normality.
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| Fund Project:the National Natural Science Foundation of China (10161004), the Natural Science Foundation of Jiangxi (0611068) and Science Foundation of Shangrao Normal College. |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2006.03.005 |
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