Abstract

A general representation of quadratic expressions in possibly singular elliptically contoured random vectors, as well as a procedure for the numerical evaluation of their distributions, are proposed in this paper. First, such quadratic expressions are represented as the difference of two positive definite elliptically contoured quadratic forms plus an independently distributed linear combination of spherically distributed random variables. Their distributions are then determined from a representation of elliptically contoured vectors in terms of scale mixtures of Gaussian vectors. Quadratic forms and quadratic expressions in various types of  elliptically contoured vectors are considered. An accurate moment-based approximation to their density function is also provided. Several  numerical examples illustrate the results.

 

 

This work is licensed under a Creative Commons Attribution 4.0 License.