论文标题
无效正常近似准确性的边界
Bounds for the accuracy of invalid normal approximation
论文作者
论文摘要
在应用概率中，正常近似通常用于具有假定的加性结构的数据分布。该传统基于（独立）随机变量的总和的中心极限定理。但是，在观察到的样本量有限时，几乎不可能检查提供中心极限定理有效性的条件。因此，在使用理论上不适用的情况下，知道正常近似的真实准确性是什么非常重要。此外，在某些情况下，与计算机仿真相关，如果总和中单独的求和分布属于吸引稳定定律的吸引域，特征指数小于两个，则观察到的归一量和正常定律的分布与正常定律之间的距离首先减少，因为夏季的数量仅在夏季的数量增加时就会增加。在本文中，试图对这种影响给出一些理论上的解释。
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is practically impossible to check the conditions providing the validity of the central limit theorem when the observed sample size is limited. Therefore it is very important to know what the real accuracy of the normal approximation is in the cases where it is used despite it is theoretically inapplicable. Moreover, in some situations related with computer simulation, if the distributions of separate summands in the sum belong to the domain of attraction of a stable law with characteristic exponent less than two, then the observed distance between the distribution of the normalized sum and the normal law first decreases as the number of summands grows and begins to increase only when the number of summands becomes large enough. In the present paper an attempt is undertaken to give some theoretical explanation to this effect.
