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Decomposition of the Multivariate Beta Distribution with Applications

Published online by Cambridge University Press:  20 November 2018

D. G. Kabe  and
R. P. Gupta
D. G. Kabe
Affiliation:
St. Mary's University, Halifax, Nova Scotia
R. P. Gupta
Affiliation:
Dalhousie University, Halifax, Nova Scotia
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Summary

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Let L be a positive definite symmetric matrix having a noncentral multivariate beta density of an arbitrary rank, see, e.g. Hayakawa ([2, p. 12, Equation 38]). Then an explicit procedure is given for decomposing the density of L in terms of densities of independent beta variates.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 225 - 228
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Constantine, A. G., Some noncentral distribution problems in multivariate analysis, Ann. Math. Statist. 34 (1963), 1270-1285.Google Scholar
2. Takesi, Hayakawa, On the distribution of the maximum latent root of a positive definite symmetric random matrix, Ann. Inst. Statist. Math. 19 (1967), 1-17.Google Scholar
3. Kabe, D. G., Some results on the distribution of two random matrices used in classification procedures, Ann. Math. Statist. 36 (1963), 181-185.Google Scholar
4. Khatri, C. G. and Pillai, K. C. S., Some results on the noncentral multivariate beta distribution and moments of traces of two matrices, Ann. Math. Statist. 36 (1965), 1511-1520.Google Scholar
5. Kshirsagar, A. M., Distributions associated with the factor of Wilks* A in discriminant analysis, J. Austral. Math. Soc. 10 (1969), 269-277.Google Scholar
6. Radcliffe, J., The distributions of certain factors occurring in discriminant analysis, Proc. Cambridg. Philos. Soc. 64 (1968), 731-740.Google Scholar