Geometric                package: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 `length(n) > 1', the length is
          taken to be the number required.

    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 P[X <= x],
          otherwise, P[X > x].

Details:

     The geometric distribution with `prob' = p has density

                           p(x) = p (1-p)^x

     for x = 0, 1, 2, ...

     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) >=
     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)))

