# Geometric

##### The Geometric Distribution

Density, distribution function, quantile function and random
generation for the geometric distribution with parameter `prob`

.

- Keywords
- distribution

##### Usage

```
dgeom(x, prob, log = FALSE)
pgeom(q, prob, lower.tail = TRUE, log.p = FALSE)
qgeom(p, prob, lower.tail = TRUE, log.p = FALSE)
rgeom(n, prob)
```

##### Arguments

- x, q
- vector of quantiles representing the number of failures in a sequence of Bernoulli trials before success occurs.
- p
- vector of probabilities.
- n
- number of observations. If
`length(n) > 1`

, the length is taken to be the number required. - prob
- probability of success in each trial.
`0 < prob <= 1<="" code="">.`

- log, log.p
- logical; if TRUE, probabilities p are given as log(p).
- lower.tail
- logical; if TRUE (default), probabilities are $P[X \le x]$, otherwise, $P[X > x]$.

##### Details

The geometric distribution with `prob`

$= p$ has density
$$p(x) = p {(1-p)}^{x}$$
for $x = 0, 1, 2, \ldots$, $0 < p \le 1$.

If an element of `x`

is not integer, the result of `dgeom`

is zero, with a warning.

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

##### Value

`dgeom`

gives the density,
`pgeom`

gives the distribution function,
`qgeom`

gives the quantile function, and
`rgeom`

generates random deviates.Invalid `prob`

will result in return value `NaN`

, with a warning.The length of the result is determined by `n`

for
`rgeom`

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

are recycled to the
length of the result. Only the first elements of the logical
arguments are used.
##### Source

`dgeom`

computes via `dbinom`

, using code contributed by
Catherine Loader (see `dbinom`

). `pgeom`

and `qgeom`

are based on the closed-form formulae. `rgeom`

uses the derivation as an exponential mixture of Poissons, see Devroye, L. (1986) *Non-Uniform Random Variate Generation.*
Springer-Verlag, New York. Page 480.

##### See Also

Distributions for other standard distributions, including
`dnbinom`

for the negative binomial which generalizes
the geometric distribution.

##### Examples

`library(stats)`

```
qgeom((1:9)/10, prob = .2)
Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))
```

*Documentation reproduced from package stats, version 3.1.1, License: Part of R 3.1.1*