# MultiHypergeometric

0th

Percentile

##### 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.

Hypergeometric

##### Aliases
• MultiHypergeometric
• dmvhyper
• rmvhyper
##### Examples
# NOT RUN {
# Generating 10 random draws from multivariate hypergeometric
# distribution parametrized using a vector

rmvhyper(10, c(10, 12, 5, 8, 11), 33)

# }