The Distribution of the Product of Beta Determinants
René Ehlers1, Andriëtte Bekker1, J.J.J. Roux1, Mohammad Arashi2
1Department of Statistics, University of Pretoria, South Africa; 2Faculty of Mathematics, Sharood University, Sharood, Islamic Republic of Iran

The product moments of bimatrix variate beta distributions are derived. From these, exact expressions for the distributions of statistics are obtained by using the Mellin transform. These distributions add value to multivariate statistical analysis with specific reference to factors of Wilks' statistics and the product of generalised statistics.


1. Anderson, T.W. (1984). An introduction to multivariate statistical analysis, 2nd ed., John Wiley & Sons, New York.

2. Bekker, A. Roux, J.J.J. & Arashi, M. (2011). Exact nonnull distribution of Wilks's Statistic: ratio and product of independent components. Journal of Multivariate Analysis, 102, 619-628. (

3. Bekker, A. Roux, J.J.J., Ehlers, R. & Arashi, M. (2010). The bimatrix variate beta type IV distribution: relation to Wilks's statistic and bimatrix variate Kummer-beta type IV distribution. Accepted for publication Communications in Statistics-Theory and Methods. (Status: In Production)

4. Kshirsagar, A.M. (1972). Multivariate Analysis, Marcel Dekker, New York.

5. Wilks, S.S. (1932). Certain generalizations in the analysis of variance, Biometrika, 24, 471-494.

Keywords: Bimatrix variate beta distributions; Product of beta determinants; Mellin transforms; Statistics

Biography: René Ehlers is a lecturer in Mathematical Statistics at the University of Pretoria, South Africa. Her fields of interest include matrix variate distribution theory, multivariate analysis and Bayesian statistics. The research presented here forms part her PhD studies that was recently submitted.