Geometric {stats} | R Documentation |

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

.

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)

`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` . |

`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]. |

The geometric distribution with `prob`

*= p* has density

*p(x) = p (1-p)^x*

for *x = 0, 1, 2, ...*, *0 < p <= 1*.

If an element of `x`

is not integer, the result of `pgeom`

is zero, with a warning.

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

`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.

`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.

`dnbinom`

for the negative binomial which generalizes
the geometric distribution.

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

[Package *stats* version 2.5.0 Index]