On sums of symmetrically dependent random variables
On sums of symmetrically dependent random variables
复制标题
关于对称相关随机变量的总和
DOI：
10.1080/03461238.1953.10419466
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发表时间：
1953
影响因子：
1.8
通讯作者：
E. Andersen
中科院分区：
文献类型：
--
作者：
E. Andersen
摘要1. 在一篇论文[1]中，我已经证明了一些关于对称分布随机变量之和的符号的定理。后来在一篇札记[2]中，我阐述了一些关于独立随机变量之和的符号的结果。当时承诺完整的证明将在其他地方发表。在本文中，[1]中的结果被推广。此外，D. A. 达林在[4]中针对独立变量所证明的结果被扩展到对称相关变量。还给出了[2]中所阐述的一个结果的完整证明。然而，这个结果仅限于独立变量。正是这个结果原始证明中的思路，现在构成了下面定理1证明的基础。
Abstract 1. In a paper [1] I have proved some theorems concerning the signs of sums of symmetrically distributed random variables. Later in a note [2] I have stated some results on the signs of sums of independent random variables. It was promised that complete proofs should be publisbed elsewhere. In this paper the results in [1] are generalized. Furthermore the results proved by D. A. Darling in [4] for independent variables are extended to symmetrically dependent variables. A complete proof of one of the results stated in [2] is also given. This result, however, is restricted to independent variables. It is the idea in the original proof of this result, which now forms the basis of the proof of Theorem 1 below.