Definition: Categorical distribution

Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Multivariate discrete distributions ▷ Categorical distribution ▷ Definition

Definition: Let $X$ be a random vector. Then, $X$ is said to follow a categorical distribution with success probability $p_1, \ldots, p_k$

\[\label{eq:cat} X \sim \mathrm{Cat}(\left[p_1, \ldots, p_k \right]) \; ,\]

if $X = e_i$ with probability $p_i$ for all $i = 1, \ldots, k$, where $e_i$ is the $i$-th elementary row vector, i.e. a $1 \times k$ vector of zeros with a one in $i$-th position.

 

Sources:

• Wikipedia (2020): "Categorical distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-03-22; URL: https://en.wikipedia.org/wiki/Categorical_distribution.

Metadata: ID: D46 | shortcut: cat | author: JoramSoch | date: 2020-03-22, 18:09.