where p is the number of dimensions. In the context of likelihood-ratio testsm is typically the error degrees of freedom, and n is the hypothesis degrees of freedom, so that is the total degrees of freedom.[1]
Properties
There is a symmetry among the parameters of the Wilks distribution,[1]
Approximations
Computations or tables of the Wilks' distribution for higher dimensions are not readily available and one usually resorts to approximations.
One approximation is attributed to M. S. Bartlett and works for large m[2] allows Wilks' lambda to be approximated with a chi-squared distribution
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]