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)))