| 负相协随机变量的指数不等式 |
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| 引用本文： | 邢国东,杨善朝. 负相协随机变量的指数不等式[J]. 数学物理学报(A辑), 2009, 29(6): 1679-1688 |
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| 作者姓名： | 邢国东 杨善朝 |
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| 作者单位： | 邢国东(湖南科技学院数学系,湖南永州,425100);杨善朝(广西师范大学数学学院,广西桂林,541004) |
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| 摘 要： | 该文给出了一些负相协随机变量的指数不等式.这些不等式改进了由Jabbari和Azarnoosh[4]及Oliveira[7] 所得到的相应的结果.利用这些不等式对协方差系数为几何下降情形, 获得了强大数律的收敛速度为n-1/2(log log n)1/2(log n)2.这个收敛速度接近独立随机变量的重对数律的收敛速度, 而Jabbari和Azarnoosh[4]在上述情形下得到的收敛速度仅仅为n-1/3(log n)5/3.
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| 关 键 词： | 负相协随机变量 指数不等式 收敛速度 |
| 收稿时间： | 2007-12-29 |
| 修稿时间： | 2008-12-23 |
Exponential Inequalities for Negatively Associated Random Variables |
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| Affiliation: | Department of Mathematics, Hunan University of Science and Engineering, Hunan |Yongzhou 425100 |
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| Abstract: | The authors show some exponential inequalities for negatively associated random variables. These inequalities improve the rresponding results which Jabbari and Azarnoosh (2007) and Oliveira (2005) got. As an application, the authors obtain the rate of convergence n-1/2(log log n)1/2(log n)2 for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Jabbari and Azarnoosh (2007) only got n-1/3(log n)5/3 for the case mentioned above. |
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| Keywords: | Negatively associated random variable Exponential inequality Rate of conver-gence |
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