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 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 since R version 4.0.0.

### 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.
qgeom((1:9)/10, prob = .2)