Multinomial distribution

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

Definition: Let $X$ be a random vector. Then, $X$ is said to follow a multinomial distribution with number of trials $n$ and category probabilities $p_1, \ldots, p_k$

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

if $X$ are the numbers of observations belonging to $k$ distinct categories in $n$ independent trials, where each trial has $k$ possible outcomes and the category probabilities are identical across trials.

Sources:

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

Metadata: ID: D47 | shortcut: mult | author: JoramSoch | date: 2020-03-22, 17:52.