Distributions of Central Quadratic Forms in Normal Variables: A comparison of Algorithms

Abstract

Abstract : Quadratic functions of multivariate normal random variables arise with surprising frequency in certain social science theories. However, these seem to be rarely used in applications because of the numerical difficulties in computing their distribution function for an arbitrary positive definite quadratic form in multivariate normal variables. Alternative algorithms are reviewed. Comparison trials are reported to show that the new algorithm is at least a accurate and reliable as the alternative algorithms.