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:

$$\Gamma(x;a, b)=\frac{b^a}{\Gamma(a)}x^{a-1}e^{-bx}$$ (22)

where $\Gamma(a)$ is the single-parameter Gamma function. Note, that a two-parameter gamma distribution has mean$=a/b$ and variance$=a/b^2$.