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)))