# Hypergeometric {stats}

The Hypergeometric Distribution
Package:
stats
Version:
R 3.0.2

### 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.

```m <- 10; n <- 7; k <- 8