COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 823

"Spherical Matrix Distributions and Cauchy Quotients"

Peter C.B. Phillips

February 1987

It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds.

JEL Classification: 211

Keywords: Cauchy quotients, invariant measures, matrix variates, spherical distributions