What is multinomial distribution?

Multinomial Distribution

In probability theory, the multinomial distribution is a generalization of the binomial distribution.

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Some articles on multinomial distribution:

Categorical Distribution
... A categorical distribution is a discrete probability distribution whose sample space is the set of k individually identified items ... It is the generalization of the Bernoulli distribution for a categorical random variable ... In one formulation of the distribution, the sample space is taken to be a finite sequence of integers ...
Multinomial Distribution - Related Distributions
... When k = 2, the multinomial distribution is the binomial distribution ... The continuous analogue is Multivariate normal distribution ... Categorical distribution, the distribution of each trial for k = 2, this is the Bernoulli distribution ...
Dirichlet-multinomial Distribution - Probability Mass Function - For A Multinomial Distribution Over Category Counts
... For a random vector of category counts, distributed according to a multinomial distribution, the marginal distribution is obtained by integrating out p which results in the following explicit formula ... term at the front that looks like the factor at the front of a multinomial distribution ... Another form for this same compound distribution, written more compactly in terms of the beta function, B, is as follows ...
Variational Bayesian Methods - A More Complex Example
... model described as follows Note SymDir is the symmetric Dirichlet distribution of dimension, with the hyperparameter for each component set to ... The Dirichlet distribution is the conjugate prior of the categorical distribution or multinomial distribution ... is the Wishart distribution, which is the conjugate prior of the precision matrix (inverse covariance matrix) for a multivariate Gaussian distribution ...
Dirichlet-multinomial Distribution
... In probability and statistics, the Dirichlet-multinomial distribution is a probability distribution for a multivariate discrete random variable ... It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution, which is named after George Pólya) ... It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector, and a set of discrete samples is drawn from the categorical ...

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