\begin{definition}[Definition:Gamma Distribution]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R_{\ge 0}$.
$X$ is said to have a '''Gamma distribution''' if it has probability density function: 
:$\map {f_X} x = \dfrac {\beta^\alpha x^{\alpha - 1} e^{-\beta x} } {\map \Gamma \alpha}$
for $\alpha, \beta > 0$, where $\Gamma$ is the Gamma function.
This is written: 
:$X \sim \map \Gamma {\alpha, \beta}$
\end{definition}