Showing papers on "Multivariate gamma function published in 1981"
TL;DR: In this article, the exact distribution of fp = 1−1p/11 is derived in terms of zonal polynomials, where fp is defined as the ratio of the extreme latent roots of the Wishart matrix.
Abstract: The distribution of the ratio of the extreme latent roots of the Wishart matrix is useful in testing the sphericity hypothesis for a multivariate normal population. Let X be a p×n matrix whose columns are distributed independently as multivariate normal with zero mean vector and covariance matrix ∑. Further, let S=XX′ and let 11g…g1pg0 be the characteristic roots of S. Thus S has a noncentral Wishart distribution. In this paper, the exact distribution of fp=1−1p/11 is derived. The density of fp is given in terms of zonal polynomials. These results have applications in nuclear physics also.
1 Jan 1981
TL;DR: In this article, a direct evaluation of the Wishart density as an inverse Laplace transform is presented, and it is shown that this method is easier than other methods of direct evaluation.
Abstract: Beta function of a symmetric positive definite matrix argument is usually evaluated with the help of the product rule for Laplace or generalized Mellin transforms. A direct evaluation from first principles is given in this article. It is shown that the technique helps the direct evaluation of the Wishart density as an inverse Laplace transform. It is shown that this method is easier than other methods of direct evaluation.
1 Jan 1981
TL;DR: In this paper, a characterization of the Wishart distribution using the matrix-variate beta type I as the conditional distribution was obtained using the conditional distributions of the conditional conditional distribution.
Abstract: In this paper, we obtain a characterization of the Wishart distribution using the matrix-variate beta type I as the conditional distribution.