Wilks's lambda distribution

In statistics, Wilks' lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially with regard to the likelihood-ratio test and multivariate analysis of variance (MANOVA). == Definitions == Wilks' lambda distribution is defined from two independent Wishart distributed variables as the ratio distribution of their determinants, given A ∼ W p ( Σ , m ) B ∼ W p ( Σ , n ) {\displaystyle \mathbf {A} \sim W_{p}(\Sigma ,m)\qquad \mathbf {B} \sim W_{p}(\Sigma ,n)} independent and with m ≥ p {\displaystyle m\geq p} λ = det ( A ) det ( A + B ) = 1 det ( I + A − 1 B ) ∼ Λ ( p , m , n ) {\displaystyle \lambda ={\frac {\det(\mathbf {A} )}{\det(\mathbf {A+B} )}}={\frac {1}{\det(\mathbf {I} +\mathbf {A} ^{-1}\mathbf {B} )}}\sim \Lambda (p,m,n)} where p is the number of dimensions.

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