Beta-binomial distribution

Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate discrete distributions ▷ Beta-binomial distribution ▷ Definition

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 $\beta$.

Sources:

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.