On the noncentral distribution of the ratio of the extreme roots of wishart matrix

[摘要] 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. LetXbe ap×nmatrix whose columns are distributed independently as multivariate normal with zero mean vector and covariance matrix∑. Further, letS=XX′and let11>…>1p>0be the characteristic roots ofS. ThusShas a noncentral Wishart distribution. In this paper, the exact distribution offp=1−1p/11is derived. The density offpis given in terms of zonal polynomials. These results have applications in nuclear physics also.

[学科分类] 数学（综合）