Geodesic
The Exact Non-Null Distribution of Wilks’ Λ Criterion in the Bivariate Collinear Case
Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 757-758

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Mikhail, N. N.; Tracy, D. S. The Exact Non-Null Distribution of Wilks’ Λ Criterion in the Bivariate Collinear Case. Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 757-758. doi: 10.4153/CMB-1974-136-0
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[1] 1. Consul, P. C., On some inverse Mellin transforms, Bull. Class Sc, 5e Série, 52 (1966), 547–561. Google Scholar

[2] 2. Erdelyi, A., et al., Tables of Integral Transforms, vol. 1. McGraw-Hill Book Company, Inc. (1954). Google Scholar

[3] 3. Kshirsagar, A. M., The non-central multivariate beta distribution, Ann. Math. Statist. 32 (1961), 104–111. Google Scholar

[4] 4. Malik, H. J., The distribution of the product of two noncentral beta variates, Naval Res. Logistics Quarterly 17 (1970), 327–330. Google Scholar

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