The Annals of Probability

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

Peter Hall

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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


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