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≤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:
k∏i=1pxii(where 0≤pi and ∑ipi=1)
over the support
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.