Showing papers on "Multivariate gamma function published in 2003"
TL;DR: In this paper, a class of multivariate skew distributions has been explored and its properties are derived and the relationship between theMultivariate skew normal and the Wishart distribution is studied.
28 citations
TL;DR: In this article, multivariate density expansions for the sample correlation matrix R are derived, where the density of R is expressed through multivariate normal and through Wishart distributions, and the main terms of the first three cumulants of R are obtained in matrix form.
17 citations
TL;DR: In this article, the authors extend the results on the noncentral Wishart distribution and related distributions given in Anderson (Anderson, T. W. (1946) and Dahel and Giri (1994).
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.
10 citations
TL;DR: In this article, the authors considered the case when the number of observations n is less than the dimension p of the random vectors which are assumed to be independent and identically distributed as normal with nonsingular covariance matrix.
Abstract: In this article, we consider the case when the number of observations n is less than the dimension p of the random vectors which are assumed to be independent and identically distributed as normal with nonsingular covariance matrix. The central and noncentral distributions of the singular Wishart matrix $S=XX'$, where X is the $p \times n$ matrix of observations are derived with respect to Lebesgue measure. Properties of this distribution are given. When the covariance matrix is singular, pseudo singular Wishart distribution is also derived. The result is extended to any distribution of the type $f(XX')$ for the central case. Singular multivariate beta distributions with respect to Lebesgue measure are also given.