WISHART AND PSEUDO-WISHART DISTRIBUTIONS AND SOME APPLICATIONS TO SHAPE-THEORY

Suppose that X similar to N-N x m(mu, Sigma, Theta). An expression for the density function is given when Sigma greater than or equal to 0 a nd/or Theta greater than or equal to 0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a ma trix Z of order N x m when the rank (Z) = q less than or equal to min( N, m). This paper fills an important gap in unifying, for the first ti me, all Wishart and pseudo-Wishart distributions, whether central or n oncentral, whether singular or nonsingular, and applying them in shape analysis. In particular, the shape density and the size-and-shape con e density are obtained for the singular general case. (C) 1997 Academi c Press.