Definition:Gamma Distribution

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Let $X$ be a continuous random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

Let $\operatorname{Im} \left({X}\right) = \R_{\ge 0}$.

$X$ is said to have a Gamma distribution if it has probability density function:

$\displaystyle f_X\left({x}\right) = \frac{ \beta^\alpha x^{\alpha - 1} e^{-\beta x} } {\Gamma \left({\alpha}\right)}$

for $\alpha, \beta > 0$, where $\Gamma$ is the Gamma function.

This is written:

$X \sim \Gamma \left({\alpha, \beta}\right)$

Also see

  • Results about the Gamma distribution can be found here.