stats (version 3.6.2)

# 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.

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, \(P[X > x]\).

## 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.

Distributions for other standard distributions, including `dnbinom` for the negative binomial which generalizes the geometric distribution.
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