On the Accuracy of Gaussian Approximation to the Distribution Functions of Sums of Independent Variables
On the Accuracy of Gaussian Approximation to the Distribution Functions of Sums of Independent Variables
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论自变量之和分布函数的高斯逼近精度
DOI：
10.1137/1111061
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发表时间：
1966
影响因子：
0.6
通讯作者：
I. A. Ibragimov
中科院分区：
文献类型：
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作者：
I. A. Ibragimov
在整篇文章中，我们考虑具有公共分布函数(Df)F(X)和特征函数(Cf)f(T)的同分布的独立随机变量序列1，2，‘“，n。变量N也被假定属于正态定律的吸引域。这意味着可以选择归一化常数的两个数值序列{An}和{Bn}，使得当n00时，
Throughout the entire article we consider a sequence of identicallydistributed independent random variables 1, 2,’"", n," with commondistribution function (df) F (x) and characteristic function (cf) f (t). The variables nare also assumed to belong to the domain of attraction of the normal law. This means that two numerical sequences {An} and {Bn} of normalizing constants can be chosen so that, as n oo,