APPROXIMATING BY THE WISHART DISTRIBUTION

Approximations of density functions are considered in the multivariate case. The results are presented with the help of matrix derivatives, powers of Kronecker products and Taylor expansions of functions with m atrix argument. In particular, an approximation by the Wishart distrib ution is discussed. It is shown that in many situations the distributi ons should be centred. The results are applied to the approximation of the distribution of the sample covariance matrix and to the distribut ion of the non-central Wishart distribution.