Geometric {stats}

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. 0 < prob <= 1.
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 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.

Invalid prob will result in return value NaN, with a warning.

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

dnbinom for the negative binomial which generalizes the geometric distribution.

Examples

qgeom((1:9)/10, prob = .2)
Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))

---