Limit Theorems for Densities and Asymptotic Expansions for Distributions of Sums of Independent Random Variables
Limit Theorems for Densities and Asymptotic Expansions for Distributions of Sums of Independent Random Variables
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独立随机变量和分布的密度极限定理和渐近展开式
DOI：
10.1137/1110074
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发表时间：
1965
影响因子：
0.6
通讯作者：
V. A. Statulyavichus
中科院分区：
文献类型：
--
作者：
V. A. Statulyavichus
进一步假设（定理5除外）变量j的分布具有密度。随机变量的分布函数用相应的密度bypc和特征函数bye表示，分别表示（0，1）-正态分布和密度函数。我们还需要对称化的分布函数（）（+）d（），它的相应密度和特征函数f（t）] f（t）。根据定义，序列（1.1）满足中心极限定理（clt），如果和密度的极限定理（1。td）if（.）su z（）-e（）0 as
It is further assumed (except in Theorem 5) that the distributions of the variables j have a density. The distribution function of a random variable is denoted by the corresponding density bypc and the characteristic function bye, and denote (0, 1)-normal distribution and density functions, respectively. We shall need still the symmetrized distribution function ()(+) d (), its corresponding density and characteristic function f (t)] f (t). By definition, the sequence (1.1) satisfies the central limit theorem (clt) if and the limit theorem for densities (1. td) if (.) su z ()-e () 0 as