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

This paper is concerned with the distributions of linear functions of independent U and F variates. The statistics Up,q,n is defined as U = Q1/Q1 + Q2, where Q1 and Q2 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.