Before revision:  This paper presents a novel numerical procedure to efficiently compute the moments of a given quadratic form. Based on that, a gamma distribution with matched skewness-kurtosis ratio is proposed to approximate its distribution.
After revision:  This paper presents a novel numerical procedure to efficiently compute the moments of the quadratic forms. Second, we establish a general moment-matching framework for distribution approximation, which covers existing approximation methods for the distributions of the quadratic forms of Gaussian variables. Under this framework, a novel moment-ratio method (MR) is proposed to approximate its distribution.