Geometric {base}

R Documentation

The Geometric Distribution

Description

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

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.
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

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) \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.

See Also

dnbinom for the negative binomial which generalizes the geometric distribution.

Examples

pp <- sort(c((1:9)/10, 1 - .2^(2:8)))
print(qg <- qgeom(pp, prob = .2))
## test that qgeom is an inverse of pgeom
print(qg1 <- qgeom(pgeom(qg, prob=.2), prob =.2))
all(qg == qg1)
Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))

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