Multinomial Distribution

Topics: Probability

Definition

The Multinomial Distribution is a discrete probability distribution with parameters $n$ and $k$. It consists of $n$ independent trials each of which ends with the success of one of $k$ possible outcomes.
The multinomial distribution gives the probability of any particular combination of number of successes for the various categories.

Special Cases

The following distributions are special cases of the multinomial distribution:

• Bernoulli Distribution: $k=2,\;n=1$
• Binomial Distribution: $k=2,\;n>1$
• Categorical Distribution: $k>2,\;n=1$

References

1. https://en.wikipedia.org/wiki/Multinomial_distribution