Index: The Book of Statistical Proofs ▷ Statistical Models ▷ Frequency data ▷ Dirichlet-distributed data ▷ Definition

Definition: Dirichlet-distributed data are defined as a set of vectors of proportions $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ where

\[\label{eq:dir-def} \begin{split} y_i &= [y_{i1}, \ldots, y_{ik}], \\ y_{ij} &\in [0,1] \quad \text{and} \\ \sum_{j=1}^k y_{ij} &= 1 \end{split}\]

for all $i = 1,\ldots,n$ (and $j = 1,\ldots,k$) and each $y_i$ is independent and identically distributed according to a Dirichlet distribution with concentration parameters $\alpha = [\alpha_1, \ldots, \alpha_k]$:

\[\label{eq:dir-data} y_i \sim \mathrm{Dir}(\alpha), \quad i = 1, \ldots, n \; .\]
 
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Metadata: ID: D104 | shortcut: dir-data | author: JoramSoch | date: 2020-10-22, 05:06.