Definition: Gamma distribution
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Gamma distribution ▷
Definition
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Metadata: ID: D7 | shortcut: gam | author: JoramSoch | date: 2020-02-08, 23:29.
Definition: Let $X$ be a random variable. Then, $X$ is said to follow a gamma distribution with shape $a$ and rate $b$
\[\label{eq:gam} X \sim \mathrm{Gam}(a, b) \; ,\]if and only if its probability density function is given by
\[\label{eq:gam-pdf} \mathrm{Gam}(x; a, b) = \frac{b^a}{\Gamma(a)} x^{a-1} \exp[-b x], \quad x > 0\]where $a > 0$ and $b > 0$, and the density is zero, if $x \leq 0$.
- Koch, Karl-Rudolf (2007): "Gamma Distribution"; in: Introduction to Bayesian Statistics, Springer, Berlin/Heidelberg, 2007, p. 47, eq. 2.172; URL: https://www.springer.com/de/book/9783540727231; DOI: 10.1007/978-3-540-72726-2.
Metadata: ID: D7 | shortcut: gam | author: JoramSoch | date: 2020-02-08, 23:29.