On an Approximation to the Distribution of Product of Independent Beta Variates

  • Hea Jung Kim (Department of Statistics, Dongguk University, Seoul 100-715, Korea)
  • Published : 1994.12.01

Abstract

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

Keywords

References

  1. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables Abramovitz, M.;Stegun, I.
  2. An Introduction to Multivariate Analysis Anderson, T. W.
  3. Biometrika v.36 A general distribution theory for a class of likelihood ratio criteria Box, G. E. P.
  4. Bayesian Inference in Statistical Analysis Box, G. E. P.;Tiao, G. C.
  5. Handbook of Statistics v.2 Growth curve analysis Geisser, S.;P. R. Krishnaiah(ed.)
  6. Distribution in Statistics : Continuous Multivariate Distributions in Statistics Johnson, N. L.;Kotz, S.
  7. Communications in Statistics : Theory and Methods v.15 On a GMANOVA model likelihood ratio test criterion Kabe, D. G.
  8. Proceedings of the Cambridge Philosophical Society v.57 Some extensions of the multivariate t-distribution and the multivariate generalization of the distribution of the regression coeffiecients Kshirsagar, A. M.
  9. Biometrika v.67 A normal approximation for the distribution of the likelihood ratio statistics in multivariate analysis of variance Mudholkar, G. S.;Trivedi, M. C.
  10. Handbook of Statistics Bayesian inference in MANOVA Press, S. J.;P. R. Krishnaiah(ed.)
  11. Applied Multivariate Analysis : Using Bayesian and Frequentist Methods of Inference Press, S. J.
  12. Biometrika v.35 Testing of significance in multivariate analysis Rao. C. R.