Gamma Distribution

$x$ has a two-parameter gamma distribution, denoted by $Ga(a,b)$, with parameters $a$ and $b$, if its density is given by:

$$f_{Ga}(x;a, b)=\frac{b^a}{\Gamma(a)}x^{a-1}e^{-bx}$$ (26)

where $\Gamma(a)$ is the Gamma function. Note, that a gamma distribution has $mean=a/b$ and $variance=a/b^2$. The mode of the Gamma distribution is given by:

$$mode = \frac{1}{b}(a-1)$$ (27)