# What is meant by categorical distribution?

Is it a separate type of distribution (EX: Binomial,bernoulli, Multinomial) or any distribution that can be represented this way? Can someone elaborate with a simple example

The categorical distribution is the generalization of the Bernoulli distribution to a fixed number $2 \le k$ of outcomes.

Equivalently, it is the special case of the multinomial distribution where the number of “choices” $n$ is fixed at one.

Therefore, it has pdf:

over the support

where

In summary, Bernoulli has $k=2, n=1$, binomial has $k=2, n\ge 1$, multinomial has $k\ge2, n\ge1$, and categorical has $k\ge2, n=1$.