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# 3.16. Multinomial Distribution

Applies to: @RISK 5.x and newer

Does @RISK have a multinomial distribution?

The multinomial distribution is a generalized form of the binomial distribution. In a binomial, you have a fixed sample size or number of trials, n. Every member of the population falls into one of two categories, usually called "success" and "failure". The probability of success on any trial is p, and the probability of failure on any trial is 1–p. The RiskBinomial distribution takes the parameters n and p, and at each iteration it returns a number of successes. The number of failures in that iteration is implicitly n minus the number of successes.

In a multinomial, you have three or more categories, and a probability is associated with each category. The total of the probabilities is 1, since each member of the population must be a member of some category. As with the binomial, you have a fixed sample size, n. At each iteration you want the count of each category, and the total of those counts must be n.

@RISK doesn't have a multinomial distribution natively, but you can construct one using binomial distributions and some simple logic. This workbook shows you how to do it.

Last edited: 2016-03-18