The Noncentral Wishart Distribution and Related Distributions

Abstract

In this article, we extend the results on the noncentral Wishart distribution and related distributions given in Anderson (Anderson, T. W. (1946). The noncentral Wishart distribution and certain problems multivariate statistics. Ann. Math. Statist. 17:409–431) and Dahel and Giri (Dahel, S., Giri, N. (1994). Some distribution related to a noncentral Wishart distribution. Commun. Statist.—Theory Meth. 23:229–237). Let and A = Y′Y where y_(i) is an m × 1 random vector and independently follows a normal distribution . For a more general matrix than that considered by Dahel and Giri (1994), we derive a kind of the density function of the noncentral Wishart distribution, and give the distributions of the Bartlett's decomposition, the determinant and the trace of A.

Keywords:

• Bartlett's decomposition
• Normal distribution
• Wishart distribution

Acknowledgments

The authors would like to thank the referee for helpful comments. This research was supported by NSFC, EYNSFC and RFDP.