Definition: Beta distribution
Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate continuous distributions ▷ Beta distribution ▷ Definition
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Metadata: ID: D53 | shortcut: beta | author: JoramSoch | date: 2020-05-10, 20:29.
Definition: Let $X$ be a random variable. Then, $X$ is said to follow a beta distribution with shape parameters $\alpha$ and $\beta$
\[\label{eq:beta} X \sim \mathrm{Bet}(\alpha, \beta) \; ,\]if and only if its probability density function is given by
\[\label{eq:beta-pdf} \mathrm{Bet}(x; \alpha, \beta) = \frac{1}{\mathrm{B}(\alpha, \beta)} \, x^{\alpha-1} \, (1-x)^{\beta-1}\]where $\alpha > 0$ and $\beta > 0$, and the density is zero, if $x \notin [0,1]$.
- Wikipedia (2020): "Beta distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-05-10; URL: https://en.wikipedia.org/wiki/Beta_distribution#Definitions.
Metadata: ID: D53 | shortcut: beta | author: JoramSoch | date: 2020-05-10, 20:29.