Is there any result showing that a sum of independent Wishart with same degrees of freedom but different scale matrices is a Wishart?
For example, if I have two random variables: $$ Y \sim W_p(n,\sigma_1)\ \\ X \sim W_p(n, \sigma_2), $$
where $p$ is the dimension of matrices, will $Y+X$ be equal to $W_p(n, \sigma_1 + \sigma_2)$?
