Multinomial distributions

The Multinomial distribution generalizes the Binomial distribution. A multinomial distribution describes n independent experiments, and each experiment has more than two choices. Let’s see a few real-world examples.

The real-world examples

In the binomial distribution, we use a coin-flipping example that has two outcomes – 1 and 0. Now, instead of a coin, let’s use a dice that has six outcomes. The dice-throwing example is a perfect example of a multinomial distribution.

The formal definition of a multinomial distribution

The multinomial distribution is an extension of the binomial distribution. It extends Eq. (2) to multiple outcomes, as shown in Eq. (3):

P(x 1, ⋯ , x k; n, p) =  n ! _ x 1 !x 2 !⋯ x k !  p 1 x 1⋯p k x k Eq. (3)

Let’s suppose a person throws a dice n times. Let p i be the probability of numbers...