島根大学文理学部紀要. 理学科編

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島根大学文理学部紀要. 理学科編 2
1969-03-10 発行

行列成分のΓ-分布とその関連分布について

On the Γ-distribution of Matrix Argument and Its Related Distributions
麻生 泰弘
ファイル
内容記述(抄録等)
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].