Density, distribution function, quantile function and random
generation for the geometric distribution with parameter `prob`

.

```
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)
```

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

`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.

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.

```
# NOT RUN {
qgeom((1:9)/10, prob = .2)
Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))
# }
```

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