The multinomial distribution provides a probability distribution over three or more possible outcomes. It generalizes the more fundamental binomial distribution (two outcomes).
In probability theory, the multinomial distribution generalizes the binomial distribution to three or more outcomes.
Suppose two chess players had played numerous games, from which we estimate that Player A would win with probability 0.40, Player B would win with probability 0.35, and the probability that the game ends in a draw is 0.25. The multinomial distribution can be used to answer questions like:
- If these two chess players played 12 games, what is the expected number of wins, losses, and draws for player A?
- If these two chess players play 3 games, what is the probability that A wins one, B, wins one, and they draw on the other?
Binary classification/prediction methods (such as logistic regression) can also be generalized for multinomial outcomes (i.e., three or more class labels). Multinomial logistic regression is also sometimes called a maximum entropy (MaxEnt) model.
