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

Answer

The categorical distribution is the generalization of the Bernoulli distribution to a fixed number 2k 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:

ki=1pxii(where 0pi and ipi=1)
over the support
xi{0,1}
where
n

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.

Attribution
Source : Link , Question Author : subha , Answer Author : Neil G

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