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.