In this paper we derive a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector. Using this result, the expressions of the density function as well as of the characteristic function are established. Moreover, the derived stochastic representation is used to generate random samples from product which leads to a considerable improvement in the computation efficiency. Finally, we present several important properties of the singular Wishart distribution, like its characteristic function and distributional properties of the partitioned singular Wishart matrix.
