Density, distribution function, quantile function and random
generation for the geometric distribution with parameter
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)
vector of quantiles representing the number of failures in a sequence of Bernoulli trials before success occurs.
vector of probabilities.
number of observations. If
probability of success in each trial.
logical; if TRUE, probabilities p are given as log(p).
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
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.
prob will result in return value
NaN, with a warning.
The length of the result is determined by
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.
rgeom returns a vector of type integer unless generated
values exceed the maximum representable integer when
values are returned since R version 4.0.0.
dgeom computes via
dbinom, using code contributed by
Catherine Loader (see
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.
qgeom((1:9)/10, prob = .2) Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))
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