I have a question about the inverse Wishart matrix. In my understanding, consider $\mathbf H$ is a $n\times n$ matrix with each elements are complex Gaussian with zero mean unit variance. Then $\mathbf H^* \mathbf H$ ($^*$ is Hermitian transpose) should be Wishart distribution $W_n(n, \mathbf I_n)$ and $(\mathbf H^* \mathbf H)^{-1}$ is inverse Wishart distribution $W^{-1}(\mathbf I_n, n)$.
I'm wondering how to find the order statistics distribution (or joint density function or marginal distribution) of the diagonal terms of the matrix $(\mathbf H^* \mathbf H)^{-1}$. I found that the marginal distribution of diagonal terms is inverse gamma (still try to derive it by myself). I still need to found the joint density function or ordered distribution.