A Characterization of the Wishart Distribution
A Characterization of the Wishart Distribution
It is known that if $X$ and $Y$ are independent random variables having a Gamma distribution with parameters $(\theta, n)$ and $(\theta, m)$, i.e., with density function $p(x, \theta, n) = \frac{\theta^{n/2}x^{n/2 - 1}e^{-(\frac{1}{2})\theta x}}{2^{n/2}\Gamma(n/2)},\quad 0 < x, \theta; 1 \leqq n,$ then $X + Y$ and $X/(X + Y)$, …