In this study, the multi-parameter exponential family of distribution has been used to approximate the distribution of indefinite quadratic forms in normal random vectors. Moments of quadratic forms can be obtained in any orders in terms of representation of the quadratic forms as weighted sum of non-central chi-square random variables. By Stein's identity in exponential family, we estimated parameters of probability density function. The method handled in some examples and we indicated this method suitable for approximating the quadratic form distribution.
Rekabdar G, Chinipardaz R, Mansouri B. On Approximating the Distribution of Indefinite Quadratic Forms by Moments Approach. JSS 2019; 13 (1) :157-171 URL: http://jss.irstat.ir/article-1-385-en.html