On the noncentral distribution of the ratio of the extreme roots of wishart matrix. (1981) - Waikar, V. B.
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. LetX be ap × n matrix whose columns are distributed independently as multivariate normal with zero mean vector and covariance matrix∑ . Further, letS = X X ′ and let1 1 > … > 1 p > 0 be the characteristic roots ofS . ThusS has a noncentral Wishart distribution. In this paper, the exact distribution off p = 1 − 1 p / 1 1 is derived. The density off p is given in terms of zonal polynomials. These results have applications in nuclear physics also.