On Approximating the Distribution of Indefinite Quadratic Forms by Moments Approach

‎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.