## The Annals of Probability

- Ann. Probab.
- Volume 11, Number 4 (1983), 1028-1036.

### Chi Squared Approximations to the Distribution of a Sum of Independent Random Variables

#### Abstract

We suggest several Chi squared approximations to the distribution of a sum of independent random variables, and derive asymptotic expansions which show that the error of approximation is of order $n^{-1}$ as $n \rightarrow \infty$. The error may be reduced to $n^{-3/2}$ by making a simple secondary approximation.

#### Article information

**Source**

Ann. Probab., Volume 11, Number 4 (1983), 1028-1036.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993451

**Digital Object Identifier**

doi:10.1214/aop/1176993451

**Mathematical Reviews number (MathSciNet)**

MR714965

**Zentralblatt MATH identifier**

0525.60028

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60G50: Sums of independent random variables; random walks 62E20: Asymptotic distribution theory

**Keywords**

Approximation asymptotic expansion central limit theorem Chi squared rate of convergence sums of independent random variables

#### Citation

Hall, Peter. Chi Squared Approximations to the Distribution of a Sum of Independent Random Variables. Ann. Probab. 11 (1983), no. 4, 1028--1036. doi:10.1214/aop/1176993451. https://projecteuclid.org/euclid.aop/1176993451