Gamma Distribution

Def Gamma Distribution Given parameters shape $\alpha >0$ and rate $\beta >0$, the distribution density function for gamma distribution is $f(x\mid \alpha ,\beta )=\frac{x^{\alpha -1}{e}^{-\beta x}{\beta }^{\alpha }}{\Gamma (\alpha )}\text{for }x>0$where $\Gamma$ is the gamma function, written as $X\sim \mathrm{Gamma}(\alpha ,\beta )$.

Prop The mean of gamma distribution is given by the division of its shape and rate parameters: $\mu =\alpha /\beta$. The variance is ${\sigma }^2=\alpha /{\beta }^2$.