The Noncentral Wishart Distribution and Related Distributions

Abstract

Abstract In this article, we extend the results on the noncentral Wishart distribution and related distributions given in Anderson (Anderson, T. W. (1946 Anderson, T. W. 1946. The noncentral Wishart distribution and certain problems multivariate statistics. Ann Math Statist., 17: 409–431. [Crossref] , [Google Scholar]). The noncentral Wishart distribution and certain problems multivariate statistics. Ann. Math. Statist. 17:409–431) and Dahel and Giri (Dahel, S., Giri, N. (1994 Dahel, S. and Giri, N. 1994. Some distribution related to a noncentral Wishart distribution. Commun Statist.—Theory Meth., 23: 229–237. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). 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 Dahel, S. and Giri, N. 1994. Some distribution related to a noncentral Wishart distribution. Commun Statist.—Theory Meth., 23: 229–237. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), 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.