# Multinomial mixture model

A multinomial mixture model is a mixture of multinomial distributions.

The Wikipedia page for the multinomial distribution notes the following regarding the relationship between the multinomial distribution and the categorical distribution:

Note that, in some fields, such as natural language processing, the categorical and multinomial distributions are conflated, and it is common to speak of a “multinomial distribution” when a categorical distribution is actually meant. This stems from the fact that it is sometimes convenient to express the outcome of a categorical distribution as a “1-of-$$K$$” vector (a vector with one element containing a 1 and all other elements containing a 0) rather than as an integer in the range $$1\dots K} 1 \dots$$; in this form, a categorical distribution is equivalent to a multinomial distribution over a single trial.

This is important to remember when reading about categorical mixture models versus multinomial mixture models.