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).
[1] There is a symmetry among the parameters of the Wilks distribution,[1] Computations or tables of the Wilks' distribution for higher dimensions are not readily available and one usually resorts to approximations.
[1][3] The distribution can be related to a product of independent beta-distributed random variables As such it can be regarded as a multivariate generalization of the beta distribution.
It follows directly that for a one-dimension problem, when the Wishart distributions are one-dimensional with
(i.e., chi-squared-distributed), then the Wilks' distribution equals the beta-distribution with a certain parameter set, From the relations between a beta and an F-distribution, Wilks' lambda can be related to the F-distribution when one of the parameters of the Wilks lambda distribution is either 1 or 2, e.g.,[1] and