行列成分のΓ-分布とその関連分布について

Recently we have many results of the distribution of the quadratic forms of vector variates with multivariate normal distribution after A. T. James and others. These distributions are related to the Wishart distribution. The Wishart distribution play the analogous role to the Chi-square distribution in the univariate case. C. S. Herz [H] discusses exhaustively properties of the Bessel function of matrix argument. It is well known that we can derive the Γ-distribution, the B-distribution and the F-distribution in the unified manner in the univariate case. In this paper, we treat the unified derivation of the Γ-distribution, the B-distribution and the F-distribution of matrix argument. Some results may be contained in the paper by I.･Olkin and H. Rubin [O].