Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ Beta distribution ▷ Definition

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 $x \notin [0,1]$.


Metadata: ID: D53 | shortcut: beta | author: JoramSoch | date: 2020-05-10, 20:29.