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**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

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