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 \(k=\sum_{i=1}^m x_i\),
\(N=\sum_{i=1}^m n_i\) and \(k \le N\).
References
Gentle, J.E. (2006). Random number generation and Monte Carlo methods. Springer.