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The Exact Non-Null Distribution of Wilks’ Λ Criterion in the Bivariate Collinear Case

Published online by Cambridge University Press:  20 November 2018

N. N. Mikhail  and
D. S. Tracy
N. N. Mikhail
Affiliation:
University of Windsor, Windsor, Ontario
D. S. Tracy
Affiliation:
University of Windsor, Windsor, Ontario
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It is well-known that Wilks’ Λ criterion is distributed as the product of p independent beta variables in the p-variable null-case [3]. In the collinear case, Λ is still distributed as the product of p independent beta variables, one of them following a non-central beta density. Thus when p=2, the exact non-null distribution of Λ in the collinear case is given by the product of two independent beta variables, one central and the other having non-centrality parameter λ.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 757 - 758
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Consul, P. C., On some inverse Mellin transforms, Bull. Class Sc, 5e Série, 52 (1966), 547–561.Google Scholar
2. Erdelyi, A., et al., Tables of Integral Transforms, vol. 1. McGraw-Hill Book Company, Inc. (1954).Google Scholar
3. Kshirsagar, A. M., The non-central multivariate beta distribution, Ann. Math. Statist. 32 (1961), 104–111.Google Scholar
4. Malik, H. J., The distribution of the product of two noncentral beta variates, Naval Res. Logistics Quarterly 17 (1970), 327–330.Google Scholar