# MultiHypergeometric

##### Multivariate hypergeometric distribution

Probability mass function and random generation for the multivariate hypergeometric distribution.

- Keywords
- distribution

##### Usage

`dmvhyper(x, n, k, log = FALSE)`rmvhyper(nn, n, k)

##### Arguments

- x
\(m\)-column matrix of quantiles.

- n
\(m\)-length vector or \(m\)-column matrix of numbers of balls in \(m\) colors.

- k
the number of balls drawn from the urn.

- log
logical; if TRUE, probabilities p are given as log(p).

- nn
number of observations. If

`length(n) > 1`

, the length is taken to be the number required.

##### Details

Probability mass function $$ f(x) = \frac{\prod_{i=1}^m {n_i \choose x_i}}{{N \choose k}} $$

The multivariate hypergeometric distribution is generalization of
hypergeometric distribution. It is used for sampling *without* replacement
\(k\) out of \(N\) marbles in \(m\) colors, where each of the colors appears
\(n_i\) times. Where \(k=\sum_{i=1}^m x_i\),
\(N=\sum_{i=1}^m n_i\) and \(k \le N\).

##### References

Gentle, J.E. (2006). Random number generation and Monte Carlo methods. Springer.

##### See Also

##### Examples

```
# NOT RUN {
# Generating 10 random draws from multivariate hypergeometric
# distribution parametrized using a vector
rmvhyper(10, c(10, 12, 5, 8, 11), 33)
# }
```

*Documentation reproduced from package extraDistr, version 1.8.11, License: GPL-2*