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

V. B. Waikar

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-8

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 = X X ′ and let 1 1 > … > 1 p > 0 be the characteristic roots of S . Thus S has a noncentral Wishart distribution. In this paper, the exact distribution of f p = 1 − 1 p / 1 1 is derived. The density of f p is given in terms of zonal polynomials. These results have applications in nuclear physics also.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:434306

DOI: 10.1155/S0161171281000100

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