Some remarks on \({\mathcal U}(p;m,n)\) distributions
For independent \(p\)-dimensional random vectors \(X_i\), \(i=1,\dots,n\), each having standard normal distribution \(N(0,I)\), the distribution of the \(p\times p\) random matrix \(\sum_{i=1}^nX_iX_i'\) is called the Wishart distribution \(W_p(n)\). A random variable \(U\) has distribution \({\mathcal U}(p;m,n)\) if it is equal in distribution to \(|W_1|/|W_1+W_2|\) for two independent \(p\times p\) random matrices \(W_1, W_2\) having the distributions \(W_p(n)\) and \(W_p(m)\) with \(m+n>p\). In the paper under review simple proofs are given for several known properties of \({\mathcal U}(p;m,n)\) distributions.
scientific article; zbMATH DE number 1031720