Geometric {stats}

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 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.

rgeom returns a vector of type integer unless generated values exceed the maximum representable integer when double values are returned.

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 Poisson distributions, 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

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