Wilks's lambda distribution
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In statistics, Wilks's 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). It is a multivariate generalization of the univariate F-distribution, generalizing the F-distribution in the same way that the Hotelling's T-squared distribution generalizes Student's t-distribution.
independent and with
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 is the total degrees of freedom.