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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:

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

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