The categorical distribution, also called the generalized Bernoulli distribution or multinoulli distribution, is the discrete
distribution of a single outcome from 
possible categories. If category 
has probability 
, where 
and 
, then a categorically distributed random
variable 
satisfies, for 
,
 |
The categorical distribution is the multinomial distribution with one trial. Equivalently, it can be represented by a vector
having exactly one component equal to 1 and all other components equal to 0. For
,
it reduces to the Bernoulli distribution
after the two categories are labeled 0 and 1.
