Categorical distribution
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A categorical distribution is the most general distribution whose sample space is the set {1, 2, ..., n}.
It is the generalization of the Bernoulli distribution for a categorical random variable.
It should not be confused with the multinomial distribution.
Consider the extended analogy:
Bernoulli random variable : Bernoulli distribution : Binomial distribution :: Categorical random variable : Categorical distribution : Multinomial distribution
The distribution is completely given by the probabilities associated with each number k: pk = P(X = k), k = 1,...,n.
In the BUGS software, this distribution is represented as:
BUGS: r ~ dcat(p[]) // BUGS assigns categories the values 1, 2, ..., K
Sufficient statistics from n independent observations are number of trials and count (or, equivalently, proportion) of observations in each category.
Conjugate prior is the Dirichlet distribution.
