To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Wilks's lambda distribution

From Wikipedia, the free encyclopedia

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).


Wilks' lambda distribution is defined from two independent Wishart distributed variables as the ratio distribution of their determinants,[1]


independent and with

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 is the total degrees of freedom.[1]


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


Another approximation is attributed to C. R. Rao.[1][3]


There is a symmetry among the parameters of the Wilks distribution,[1]

Related distributions

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]


See also


  1. ^ a b c d e f Kanti Mardia, John T. Kent and John Bibby (1979). Multivariate Analysis. Academic Press. ISBN 0-12-471250-9.
  2. ^ M. S. Bartlett (1954). "A Note on the Multiplying Factors for Various Approximations". J R Stat Soc Ser B. 16 (2): 296–298. JSTOR 2984057.
  3. ^ C. R. Rao (1951). "An Asymptotic Expansion of the Distribution of Wilks' Criterion". Bulletin de l'Institut International de Statistique. 33: 177–180.
This page was last edited on 23 April 2021, at 15:55
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.