Southeast University,Nanjing University of Postsand Telecommunications

In this paper, we first extend the
definitions of matrix $F$ and $t$ distributions to the left
spherical distribution family, prove the density functions have no
relation with the one producing them and then show that discuss the
elliptically contoured distributions are invariant under nonsingular
matrix transformations. These distributions include the matrix Beta,
inverse Beta, Dirichlet, inverse Dirichlet, $F$ and $t$ etc. And
finally it is shown that their distribution density functions not
only have no relation with the density function generating them but
also the transformation matrix.