In this page, we’ll discuss the categorical distribution and multinomial distribution.

Let’s start with the categorical distribution. Categorical distribution is similar to Bernoulli distribution, as it represents a result of 1 trial, but has multiple outcomes (eg: rolling a dice could have 6 consequences).

Mathematically, categorical distribution is described as below.

x: outcome k: the number of potential outcomes p: probability of each outcome

Create Categorical Distribution

Let’s create a categorical distribution. We’ll create a distribution of dice roll in this page.

library(ggplot2)
dist_categorical <- data.frame(outcome = c("1","2","3","4","5","6"), probability = c(1/6,1/6,1/6,1/6,1/6,1/6))
ggplot(dist_categorical, aes(x=outcome, y= probability)) + geom_point()

As shown above, the probability of each outcome is constant (1/6).

Multinomial Distribution

Multinomial distribution is a distribution of multiple categorical trials.

Mathematically, multinomial distribution is described as below.

m: outcome k: the number of potential outcomes μ: probability of each outcome