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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 

AMS subject classification

62H10 33A15 

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References

  1. [1]
    Anderson, T. W. (1958).An Introduction to Multivariate Statistical Analysis, Wiley, New York.zbMATHGoogle Scholar
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    Mathai, A. M. (1977). On the non-null distribution of Wilks'Lmvc,Sankhyā, B,39, Part 4.Google Scholar
  3. [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.zbMATHGoogle Scholar
  4. [4]
    Nagarsenker, B. N. (1975). Percentage points of Wilks'Lvc criterion,Commun. Statist.,4, 629–641.CrossRefGoogle Scholar
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    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.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1979

Authors and Affiliations

  • A. M. Mathai
    • 1
    • 2
  • R. S. Katiyar
    • 1
    • 2
  1. 1.McGill UniversityMontrealCanada
  2. 2.University of Campinas Universidade Estadual de CampinasCampinasBrazil

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