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In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix [Formula: see text] is established in the case of arbitrary partitioning for singular and inverse Wishart distributions. Second, the density of A₂₁A₁₁⁻¹ is derived in the case of singular, non-central singular, inverse and generalized inverse Wishart distributions. The importance of the derived results is illustrated with an example from portfolio theory.