# Binomial {stats}

### Description

Density, distribution function, quantile function and random generation for the binomial distribution with parameters `size`

and `prob`

.

### Usage

dbinom(x, size, prob, log = FALSE) pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE) qbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE) rbinom(n, size, prob)

### Arguments

- x, q
- vector of quantiles.
- p
- vector of probabilities.
- n
- number of observations. If
`length(n) > 1`

, the length is taken to be the number required. - size
- number of trials (zero or more).
- prob
- probability of success on each trial.
- 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 binomial distribution with `size`

= n and `prob`

= p has density for x = 0, ..., n. Note that binomial *coefficients* can be computed by `choose`

in R.

If an element of `x`

is not integer, the result of `dbinom`

is zero, with a warning. p(x) is computed using Loader's algorithm, see the reference below.

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

### Values

`dbinom`

gives the density, `pbinom`

gives the distribution function, `qbinom`

gives the quantile function and `rbinom`

generates random deviates.

If `size`

is not an integer, `NaN`

is returned. The length of the result is determined by `n`

for `rbinom`

, 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.

### See Also

Distributions for other standard distributions, including `dnbinom`

for the negative binomial, and `dpois`

for the Poisson distribution.

### Examples

require(graphics) # Compute P(45 < X < 55) for X Binomial(100,0.5) sum(dbinom(46:54, 100, 0.5)) ## Using "log = TRUE" for an extended range : n <- 2000 k <- seq(0, n, by = 20) plot (k, dbinom(k, n, pi/10, log = TRUE), type = "l", ylab = "log density", main = "dbinom(*, log=TRUE) is better than log(dbinom(*))") lines(k, log(dbinom(k, n, pi/10)), col = "red", lwd = 2) ## extreme points are omitted since dbinom gives 0. mtext("dbinom(k, log=TRUE)", adj = 0) mtext("extended range", adj = 0, line = -1, font = 4) mtext("log(dbinom(k))", col = "red", adj = 1)

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