## The Annals of Probability

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

Peter Hall

#### 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

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