A note on a matrix inequality forgeneralized means Original Research Article

In Statistics, generalized means of positive random variables are often considered. As is well-known, the generalized mean of order α, image, is smaller (greater) than the ordinary mean if α<1 (α>1). This result can be generalized to a corresponding inequality involving matrix random variables of a specific type. In the special case when α=−1, we have a matrix inequality that has applications in various fields of Statistics. Two such applications are presented.