# Geometric

0th

Percentile

##### 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.

Distributions for other standard distributions, including dnbinom for the negative binomial which generalizes the geometric distribution.

• Geometric
• dgeom
• pgeom
• qgeom
• rgeom
##### 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 3.2.2, License: Part of R 3.2.2

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