Hypergeometric {stats} R Documentation

## The Hypergeometric Distribution

### 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.

### Value

`dhyper` gives the density, `phyper` gives the distribution function, `qhyper` gives the quantile function, and `rhyper` generates random deviates.

### References

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

### Examples

```m <- 10; n <- 7; k <- 8
x <- 0:(k+1)
rbind(phyper(x, m, n, k), dhyper(x, m, n, k))
all(phyper(x, m, n, k) == cumsum(dhyper(x, m, n, k)))# FALSE
## but error is very small:
signif(phyper(x, m, n, k) - cumsum(dhyper(x, m, n, k)), dig=3)
```

[Package stats version 2.2.1 Index]