Geometric
The Geometric Distribution
Description
Calculates density, cumulative probability, quantile, and
generate random sample for the geometric distribution (discrete).
Usage
dgeom(x, prob, log = FALSE) # density
pgeom(q, prob, lower.tail = TRUE, log.p = FALSE) # probability
qgeom(p, prob, lower.tail = TRUE, log.p = FALSE) # quantile
rgeom(n, prob) # random
Arguments
| x, q |
numeric vectors in the range [0, Inf) that specify the quantiles.
|
| p |
a numeric vector in the range [0, 1] that specifies the probabilities.
|
| n |
an integer value in the range [0, Inf) that specifies the number of random samples requested.
If the input value is not an integer, it is truncated.
If length(n) is greater than 1,
the random function returns length(n) random samples.
|
| prob |
a numeric vector in the range [0, 1] that specifies the probability of a success in a Bernoulli trial.
|
| log |
a logical value.
If FALSE (default), the density function returns the density itself.
If TRUE, it returns the log of the density.
|
| lower.tail |
a logical value.
If TRUE (default), the probability supplied to the quantile function
or returned by the probability function is P[X <= x].
If FALSE, it is P[X > x].
|
| log.p |
a logical value.
If FALSE (default), the probability supplied to the quantile function
or returned by the probability function is the probability itself.
If TRUE, it is the log of the probability.
|
Details
The distribution parameter(s) are replicated cyclically to be the same length as
the input x, q, p, or the number of random samples requested.
Missing values (NAs) in the input or the distribution parameter(s)
will cause the corresponding elements of the result to be missing.
Value
returns density (dgeom),
cumulative probability (pgeom),
quantile (qgeom), or
random sample (rgeom)
for the geometric distribution with parameter prob.
The quantile is defined as the smallest value q such that Pr(geometric random variate <= x) >= p.
Side Effects
If the .Random.seed dataset exists, the random sample function updates its value.
The random sample function creates the .Random.seed dataset if it does not exist.
Background
The geometric distribution is the discrete probability distribution of
the number of failures before the first success in a sequence of independent experiments,
each of which has two possible outcomes (yes/no) (i.e., a Bernoulli trial)
and yields success with probability prob.
It has support on the integer set {0, 1, 2, 3, …}.
See Also
Examples
rgeom(20, 0.6) #sample of size 20 with parameter 0.6