# Hypergeometric {stats}

### Description

Density, distribution function, quantile function and random generation for the hypergeometric distribution.

### Usage

dhyper(x, m, n, k, log = FALSE) phyper(q, m, n, k, lower.tail = TRUE, log.p = FALSE) qhyper(p, m, n, k, lower.tail = TRUE, log.p = FALSE) rhyper(nn, m, n, k)

### Arguments

- x, q
- vector of quantiles representing the number of white balls drawn without replacement from an urn which contains both black and white balls.
- m
- the number of white balls in the urn.
- n
- the number of black balls in the urn.
- k
- the number of balls drawn from the urn.
- p
- probability, it must be between 0 and 1.
- nn
- number of observations. If
`length(nn) > 1`

, the length is taken to be the number required. - log, log.p
- logical; if TRUE, probabilities p are given as log(p).
- lower.tail
- logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].

### Details

The hypergeometric distribution is used for sampling *without* replacement. The density of this distribution with parameters `m`

, `n`

and `k`

(named Np, N-Np, and n, respectively in the reference below) is given by p(x) = choose(m, x) choose(n, k-x) / choose(m+n, k) for x = 0, ..., k.

The quantile is defined as the smallest value x such that F(x) ≥ p, where F is the distribution function.

### Values

`dhyper`

gives the density, `phyper`

gives the distribution function, `qhyper`

gives the quantile function, and `rhyper`

generates random deviates.

Invalid arguments will result in return value `NaN`

, with a warning.

The length of the result is determined by `n`

for `rhyper`

, and is the maximum of the lengths of the numerical parameters for the other functions. The numerical parameters other than `n`

are recycled to the length of the result. Only the first elements of the logical parameters are used.

### References

Johnson, N. L., Kotz, S., and Kemp, A. W. (1992) *Univariate Discrete Distributions*, Second Edition. New York: Wiley.

### See Also

Distributions for other standard distributions.

### Examples

Documentation reproduced from R 3.0.2. License: GPL-2.