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,
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 is the total degrees of freedom.
For large m Bartlett's approximation
allows Wilks' lambda to be approximated with a Chi-square distribution
- ↑ 1.0 1.1 1.2
Mardia, K.V. (1979). Multivariate Analysis. Academic Press.
Bartlett, M.S. (1954). "A note on multiplying factors for various approximations". J. Royal Statist. Soc. Series B. 16: 296–298.
it:Variabile casuale Lambda di Wilks