| Geometric {base} | 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 |
prob |
probability of success in each trial. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
The geometric distribution with prob = p has density
p(x) = p {(1-p)}^{x}
for x = 0, 1, 2, \ldots
If an element of x is not integer, the result of pgeom
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.
See Also
dnbinom for the negative binomial which generalizes
the geometric distribution.
Examples
pp <- sort(c((1:9)/10, 1 - .2^(2:8)))
print(qg <- qgeom(pp, prob = .2))
## test that qgeom is an inverse of pgeom
print(qg1 <- qgeom(pgeom(qg, prob=.2), prob =.2))
all(qg == qg1)
Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni)))