Negative Multinomial distribution type 1 | Vose Software

# Negative Multinomial distribution type 1

Format: NegMultinomial({s}), {p})

The NegMultinomial distribution is a generalization of the NegBin distribution. The NegBin(s,p) distribution estimates the total number of binomial trials that are failures before s successes are achieved where there is a probability p of success with each trial.

For the NegMultinomial distribution, instead of having a single value for s, we now have a set of success values {s} representing different 'states' of successes (si) one can have, with each 'state' i having a probability pi of success.

Now, the NegMultinomial distribution tells us how many failures we will have before we have achieved the total number of successes.

##### Example

Suppose you want to do a telephone survey about a certain product you made by calling people you pick randomly out of the phone book.

You want to make sure that at the end of the week you have called 50 people who never heard of your product, 50 people who don't have internet at home and 200 people who use internet almost daily.

If you know the probabilities of success pi , the NegMultinomial({50,50,200},{p1,p2,p3}) will tell you how many failures you'll have before you've called all the people you wanted and so you also know the total number of phone calls you'll have to make to reach the people you wanted.

The total number of phone calls = the total number of successes (300) + the total number of failures (NegMultinomial({50,50,200},{p1,p2,p3})).

## ModelRisk functions added to Microsoft Excel for the Negative Multinomial Type 1 distribution

VoseNegMultinomial generates random values from this distribution for Monte Carlo simulation.