On the noncentral distribution of the ratio of the extreme roots of wishart matrix. (1981)

• Record Type: Journal Article
• Authors: Waikar, V. B.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 4:Number 1(1981)
• Page Start: 147
• Page End: 154
• Publication Date: 1981
• Subjects: extreme roots -- Wishart distribution -- Zonal polynomials; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171281000100
• Languages: English
• ISSNs: 0161-1712

Abstract

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.