ON ONE IDENTITY FOR DISTRIBUTION OF SUMS OF INDEPENDENT RANDOM VARIABLES

被引：0

作者：

Kruglov, V. M. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2014年 / 58卷 / 02期

关键词：

independent random variables; characteristic function; inverse formula;

D O I：

10.1137/S0040585X97986576

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In a 1957 paper F. Spitzer published, among other things, one estimate of the distribution function of sums of independent symmetric random variables with a common absolutely continuous distribution. This estimation was constructed with the help of one identity for the distribution of a sum of the above-mentioned random variables, the proof of which was not given. In this paper we prove the Spitzer identity for any independent random variables, and by using it we construct an estimate of the distribution of a sum of independent identically distributed random variables. The Spitzer estimate can be derived as a particular case of the proposed estimation.

引用

页码：329 / U190

页数：3