Concept

# Wilks's lambda distribution

Summary
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). Definition Wilks' lambda distribution is defined from two independent Wishart distributed variables as the ratio distribution of their determinants, given :\mathbf{A} \sim W_p(\Sigma, m) \qquad \mathbf{B} \sim W_p(\Sigma, n) independent and with m \ge p :\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. In the context of likelihood-ratio tests m is typically the error degrees of freedom, and n is the hypothesis degrees of freedom, so that n+m is the total degrees of freedom. Approximations Computations or tables of the Wilks' distributio
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