Advertisement

Distribution of Likelihood Criteria and Box Approximation

  • A. K. Gupta
  • J. Tang
Part of the Theory and Decision Library book series (TDLB, volume 8)

Abstract

In this paper, the exact distribution of a random variable whose moments are a certain function of gamma functions (Box, 1949), has been derived. It is shown that Box’s asymptotic expansion can be obtained from this exact distribution by collecting terms of the same order. From the point of view of computation, the derived series has a distinct advantage over the results of Box since the coefficients satisfy a recurrence relation.

Key words and phrases

Asymptotic Distribution Percentage Points Convergence Recursive Formula Test of Independence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd edition. Wiley, New York.zbMATHGoogle Scholar
  2. Box, G. E. P. (1949). ‘A General Distribution Theory for a Class of Likelihood Criteria.’ Biometrika, 36, 317–346.MathSciNetGoogle Scholar
  3. Gupta, A. K. (1977). ‘On the Distribution of Sphericity Test Criterion in the Multivariate Gaussian Distribution.’ Aust. J. Statist., 19, 202–205.zbMATHCrossRefGoogle Scholar
  4. Gupta, A. K., and Tang, J. (1984). ‘Distribution of Likelihood Ratio Statistic for Testing Equality of Covariance of Multivariate Gaussian Models.’ Biometrika, 71, 555–559.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Mathai, A. M., and Katiyar, R. S. (1979). ‘Exact Percentage Points for Testing Independence.’ Biometrika, 66, 353–356.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Mudholkar, G. S., Trivedi, M. C, and Lin, C. T. (1982). ‘An Approximation to the Distribution of Likelihood Ratio Statistic for Testing Complete Independence.’ Technometrics, 24, 139–143.zbMATHCrossRefGoogle Scholar
  7. Tang, J., and Gupta, A. K. (1984). ‘On the Distribution of the Product of Independent Beta Random Variables.’ Statist. & Probl. Letters, 2, 165–168.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Tang, J., and Gupta, A. K. (1987). ‘On the Type-B Integral Equation and the Distribution of Wilks’ Statistic for Testing Independence of Several Groups of Variables.’ Statistics, 18, (to appear).Google Scholar
  9. Walster, G. W., and Tretter, M. J. (1980). ‘Exact Noncentral Distribution of Wilks’ A and Wilks-Lawley U Criteria as Mixtures of Incomplete Beta Functions: For Three Tests.’ Ann. Statist., 8, 1388–1390.MathSciNetzbMATHCrossRefGoogle Scholar
  10. Wilks, S. S. (1932). ‘Certain Generalizations in Analysis of Variances.’ Biometrika, 24, 471–494.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • A. K. Gupta
    • 1
  • J. Tang
    • 2
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenJapan
  2. 2.Bell Communications ResearchPiscatawayUSA

Personalised recommendations