Multinomial distribution

Format: Multinomial(n,{p})

The Multinomial distribution is a multivariate distribution used to describe how many independent trials will fall into each of several categories where the probability of falling into any one category is constant for all trials.

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 can be simulated using the ModelRisk function:

{VoseMultinomial(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).

ModelRisk functions added to Microsoft Excel for the Multinomial distribution

VoseMultinomial generates random values from this distribution for Monte Carlo simulation

VoseMultinomialProb returns the probability mass or cumulative distribution function for this distribution

VoseMultinomialProb10 returns the log10 of the probability mass or cumulative distribution function  

 

 

ModelRisk

Monte Carlo simulation in Excel. Learn more

Tamara

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