Definition: Beta-binomial distribution
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The Book of Statistical Proofs ▷
Probability Distributions ▷
Univariate discrete distributions ▷
Beta-binomial distribution ▷
Definition
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Metadata: ID: D177 | shortcut: betabin | author: JoramSoch | date: 2022-10-20, 08:09.
Definition: Let $p$ be a random variable following a beta distribution
\[\label{eq:beta} p \sim \mathrm{Bet}(\alpha, \beta)\]and let $X$ be a random variable following a binomial distribution conditional on $p$
\[\label{eq:bin} X \mid p \sim \mathrm{Bin}(n, p) \; .\]Then, the marginal distribution of $X$ is called a beta-binomial distribution
\[\label{eq:betabin} X \sim \mathrm{BetBin}(n, \alpha, \beta)\]with number of trials $n$ and shape parameters $\alpha$ and $\beta$.
- Wikipedia (2022): "Beta-binomial distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2022-10-20; URL: https://en.wikipedia.org/wiki/Beta-binomial_distribution#Motivation_and_derivation.
Metadata: ID: D177 | shortcut: betabin | author: JoramSoch | date: 2022-10-20, 08:09.