Geometric: 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.

vector of probabilities.

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, $P[X > x]$.

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.

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.

Examples

Run this code

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