On the distribution of linear functions of independent F and U variates

Abstract

This paper is concerned with the distributions of linear functions of independent U and F variates. The statistics U-p,U-q,U-n is defined as U = Q(1)/Q(1) + Q(2), where Q(1) and Q(2) are p x p random matrices and independently distributed as W(Sigma,n) and W(Sigma, q), respectively. Useful and accurate approximations are considered for the linear combinations of two independent U variates as well as the linear combinations of two independent F variates.