  This paper discusses the approximate distributions of eigenvalues of a
singular Wishart matrix. We give the approximate joint density of eigenvalues
by Laplace approximation for the hyper-geometric functions of matrix arguments.
Furthermore, we show that the distribution of each eigenvalue can be
approximated by the chi-square distribution with varying degrees of freedom
when the population eigenvalues are infinitely dispersed. The derived result is
applied to testing the equality of eigenvalues in two populations
