Properties of Matrix Variate Confluent Hypergeometric Function Distribution

Abstract

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 X2-1/2X1X2-1/2, (X1+X2)-1/2X1(X1+X2)-1/2, and X1+X2, where m×m independent random matrices X1 and X2 follow confluent hypergeometric function kind 1 and gamma distributions, respectively.