Definition: Dirichlet distribution
Index:
The Book of Statistical Proofs ▷
Probability Distributions ▷
Multivariate continuous distributions ▷
Dirichlet distribution ▷
Definition
Sources:
Metadata: ID: D54 | shortcut: dir | author: JoramSoch | date: 2020-05-10, 20:36.
Definition: Let be a k \times 1 random vector. Then, X is said to follow a Dirichlet distribution with concentration parameters \alpha = \left[ \alpha_1, \ldots, \alpha_k \right]
\label{eq:Dir} X \sim \mathrm{Dir}(\alpha) \; ,if and only if its probability density function is given by
\label{eq:beta-pdf} \mathrm{Dir}(x; \alpha) = \frac{\Gamma\left( \sum_{i=1}^k \alpha_i \right)}{\prod_{i=1}^k \Gamma(\alpha_i)} \, \prod_{i=1}^k {x_i}^{\alpha_i-1}where \alpha_i > 0 for all i = 1, \ldots, k, and the density is zero, if x_i \notin [0,1] for any i = 1, \ldots, k or \sum_{i=1}^k x_i \neq 1.
- Wikipedia (2020): "Dirichlet distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-05-10; URL: https://en.wikipedia.org/wiki/Dirichlet_distribution#Probability_density_function.
Metadata: ID: D54 | shortcut: dir | author: JoramSoch | date: 2020-05-10, 20:36.