On the Exact Distributions of the Traces of S1(S1 + S2) sup (-1) and S1S2sup (-1).

摘要

In this paper,the authors derived the exact distributions of the traces of S1S2sup (-1) and S1(S1 + S2) sup (-1) where S1and S2are independently distributed as central Wishart matrices and the expected values of these matrices are the same. The method used involves expressing the Laplace transformations in terms of the linear combinations of products of certain double integrals and then taking the inverse Laplace transformations. (Author)