# Multivariate Inverse Hypergeometric distribution type 1

Format: InvMultiHypergeo({s}, {d})

The Inverse Multivariate Hypergeomeric distribution answers the question: how many extra (wasted) random multivariate hypergeometric samples will occur before the required numbers of successes {s} are selected from each sub-population {D}.

For example, imagine that our population is split up into four sub-groups {A,B,C,D} of sizes {20,30,50,10} and that we are going to randomly sample from this population until we have {4,5,2,1} of each sub-group respectively. The number of extra samples we will have to make is modeled as:

=VoseInvMultiHypergeo({4,5,2,1},{20,30,50,10})

The total number of trials that need to be performed is:

=SUM({4,5,2,1}) + VoseInvMultiHypergeo({4,5,2,1},{20,30,50,10})

The InvMultiHypergeo2 is a multivariate distribution that responds to the same question, but breaks down the number of extra samples into their sub-groups.

## ModelRisk functions added to Microsoft Excel for the Inverse Hypergeometric Type 1 distribution

VoseInvMultiHypergeo generates random values from this distribution for Monte Carlo simulation