Category:Moment Generating Function of Gamma Distribution

This category contains pages concerning Moment Generating Function of Gamma Distribution:

Let $X \sim \map \Gamma {\alpha, \beta}$ for some $\alpha, \beta > 0$, where $\Gamma$ is the Gamma distribution.

Then the moment generating function of $X$ is given by:

$\map {M_X} t = \begin {cases} \paren {1 - \dfrac t \beta}^{-\alpha} & t < \beta \\ \text {does not exist} & t \ge \beta \end {cases}$