Approximating the Distribution of Quadratic Forms Using Orthogonal Polynomials

Abstract

In this paper we propose some techniques to approximate the distribution of quadratic forms in normal random variables. The first two techniques will be based on orthogonal polynomials, namely; the Hermitte and Laguerre polynomials. The third technique will be based on a mixture of normal and truncated gamma distributions. The performance of these approximations will be studied and discussed for various quadratic forms.