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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. It is a generalization of the F-distribution, and generalizes Hotelling's T-square distribution in the same way that the F-distribution generalizes Student's t-distribution.
Wilks' lambda distribution is related to two independent Wishart distributed variables, and is defined as follows,[1]
given
independent and with 
The distribution can be related to a product of independent Beta distributed random variables
 
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.[1]
For large m Bartlett's approximation [2] allows Wilks' lambda to be approximated with a Chi-square distribution
 [1]
References
- ^ a b c Mardia, K.V.; J.T. Kent, J.M. Bibby (1979). Multivariate Analysis, Academic Press.
- ^ Bartlett, M.S. (1954). "A note on multiplying factors for various ?2 approximations". J. Royal Statist. Soc. Series B 16: 296–298.
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