Properties of matrix variate confluent hypergeometric function distribution (Q1657995)

Summary: We study matrix variate confluent hypergeometric function kind 1 distribution which is a generalization of the matrix variate gamma distribution. We give several properties of this distribution. We also derive density functions of \(X_2^{- 1 / 2} X_1 X_2^{- 1 / 2}\), \((X_1 + X_2)^{- 1 / 2} X_1(X_1 + X_2)^{- 1 / 2}\), and \(X_1 + X_2\), where \(m \times m\) independent random matrices \(X_1\) and \(X_2\) follow confluent hypergeometric function kind 1 and gamma distributions, respectively.