The inverted Dirichlet-hypergeometric function distribution (IDH) was introduced by Nagar and Bran (2009) to generalize the inverted Dirichlet distribution (Tiao and Cuttman 1965). In this paper, we derive the marginal, conditional and partial sums densities of the IDH. We also derive the joint moments of it. Furthermore, we show how to derive its density from the Dirichlet distribution. Finally, we use the Fisher’s scoring method for the estimation of parameters (Kotz et al 2000).