Chi-square approximation of squared sums of independent random variables

Abstract

In this work, we have 2 objectives. First, we find a solution of the Stein's equation for chi-square distribution with degree of freedom 1 and its properties. Second, we give bounds on chi-square approximation of the squared sums of independent random variables under the existence of the second or the third moments by using the relation between the chi-square random variable with degree of freedom 1 and the standard normal random variable.