Wilks' lambda distribution

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).

Wilks's lambda distribution is defined from two independent Wishart distributed variables as the ratio distribution of their determinants,

given

independent and with ${\displaystyle m\geq p}$

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 ${\displaystyle n+m}$ is the total degrees of freedom.

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