MultiHypergeometric: Multivariate hypergeometric distribution
Description
Probability mass function and random generation
for the multivariate hypergeometric 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 $k=sum(x)$,
$N=sum(n)$ and $k
References
Gentle, J.E. (2006). Random number generation and Monte Carlo methods. Springer.