Annals of the Institute of Statistical Mathematics

, Volume 31, Issue 2, pp 215–224

# The distribution and the exact percentage points for Wilks'Lmvc criterion

• A. M. Mathai
• R. S. Katiyar
Article

## Summary

Wilks'Lmvc is the likelihood ratio criterion for testing the hypothesis that the mean values are equal, the variances are equal and the covariances are equal, in ap-variate normal population. In this article the exact null distribution as well as the exact percentage points are given for the first time. The distribution is obtained for the most general cases and the inverse tables, namely, the values ofu for given values ofF(u) are computed for the values ofF(u)=0.01, 0.02, 0.05 and for the various values ofn andp whereF(u) is the exact distribution function of the test statistic,n=N−1 andN is the sample size. The exact tables are given forp=2, 3, 4, 5, 6, 7, 8, 9.

## Key words and phrases

Likelihood ratio criterion multinormal population exact null distribution exact percentage points

62H10 33A15

## Preview

Unable to display preview. Download preview PDF.

## References

1. 
Anderson, T. W. (1958).An Introduction to Multivariate Statistical Analysis, Wiley, New York.
2. 
Mathai, A. M. (1977). On the non-null distribution of Wilks'Lmvc,Sankhyā, B,39, Part 4.Google Scholar
3. 
Mathai, A. M. and Saxena, R. K. (1973).Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, (Lecture Notes Series 348) Springer-Verlag, Hidelberg and New York.
4. 
Nagarsenker, B. N. (1975). Percentage points of Wilks'Lvc criterion,Commun. Statist.,4, 629–641.
5. 
Wilks, S. S. (1946). Sample criteria for testing equality of means, equality of variances and equality of covariances in a normal multivariate distribution,Ann. Math. Statist.,17, 257–281.

© The Institute of Statistical Mathematics, Tokyo 1979

## Authors and Affiliations

• A. M. Mathai
• 1
• 2
• R. S. Katiyar
• 1
• 2