# Multinomial

Multinomial(n,{pi})

Multinomial equations

The Multinomial distribution is an array distribution (returns a list of generated values in each iteration, instead of one value) and is used to describe how many independent trials will fall into each of several (i.e. more than two) categories. As such, it is an extension of the Binomial distribution where there are only two possible outcomes ("successes' and, by implication, "failures').

#### Uses

For example, consider the action people might take on entering a shop:

Code

Action

Probability

A1

Enter and leave without purchase or sample merchandise

32%

A2

Enter and leave with a purchase

41%

A3

Enter and leave with sample merchandise

21%

A4

Enter to return a product and leave without purchase

5%

A5

Enter to return a product and leave with a purchase

1%

If 1000 people enter a shop, how many will match each of the above actions?

The answer is {Multinomial(1000,{32%, 41%, 21%, 5%, 1%})} which is an array function that generates five separate values. The sum of those five values must, of course, always add up to the number of trials (1000 in this example).

The topic Multivariate Trials provides some other worked examples and illustrates how to create a Multinomial distribution with different simulation software packages. In finance, Multinomial distributions are used in Markov chain models that can help in estimating credit risk.

#### Generation

How to generate the Multinomial model in different software specific packages can be found here:

Crystal Ball does not offer the Multinomial distribution directly, but is easily constructed from a set of nested Binomial distributions, as demonstrated in the model.

@RISK does not offer the Multinomial distribution directly, but is easily constructed from a set of nested Binomial distributions, as demonstrated in the model

• No labels