Evaluating the density of ratios of noncentral quadratic forms in normal variables

Evaluating the density of ratios of noncentral quadratic forms in normal variables

Two computable expressions for the exact density of a ratio of quadratic forms in Gaussian random vectors are derived, one of which is restricted to special cases of the problem. Ratios of this type are ubiquitous in econometrics, but their density, unlike the corresponding cumulative distribution function, has not received much attention to date. The new algorithms complement those available f...

The moments of products of quadratic forms in normal variables*

The expectation of the product of an arbitrary number of quadratic forms in normally distributed variables is derived.

Approximating the Distribution of Indefinite Quadratic Forms in Normal Variables by Maximum Entropy Density Estimation

I the Distributions of Quadratic Forms on Normal Random Variables

Approximating the Distributions of Singular Quadratic Expressions and their Ratios

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...