| % File src/library/stats/man/Geometric.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2020 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{Geometric} |
| \alias{Geometric} |
| \alias{dgeom} |
| \alias{pgeom} |
| \alias{qgeom} |
| \alias{rgeom} |
| \title{The Geometric Distribution} |
| \description{ |
| Density, distribution function, quantile function and random |
| generation for the geometric distribution with parameter \code{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{ |
| \item{x, q}{vector of quantiles representing the number of failures in |
| a sequence of Bernoulli trials before success occurs.} |
| \item{p}{vector of probabilities.} |
| \item{n}{number of observations. If \code{length(n) > 1}, the length |
| is taken to be the number required.} |
| \item{prob}{probability of success in each trial. \code{0 < prob <= 1}.} |
| \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} |
| \item{lower.tail}{logical; if TRUE (default), probabilities are |
| \eqn{P[X \le x]}, otherwise, \eqn{P[X > x]}.} |
| } |
| \details{ |
| The geometric distribution with \code{prob} \eqn{= p} has density |
| \deqn{p(x) = p {(1-p)}^{x}}{p(x) = p (1-p)^x} |
| for \eqn{x = 0, 1, 2, \ldots}, \eqn{0 < p \le 1}. |
| |
| If an element of \code{x} is not integer, the result of \code{dgeom} |
| is zero, with a warning. |
| |
| The quantile is defined as the smallest value \eqn{x} such that |
| \eqn{F(x) \ge p}, where \eqn{F} is the distribution function. |
| } |
| \value{ |
| \code{dgeom} gives the density, |
| \code{pgeom} gives the distribution function, |
| \code{qgeom} gives the quantile function, and |
| \code{rgeom} generates random deviates. |
| |
| Invalid \code{prob} will result in return value \code{NaN}, with a warning. |
| |
| The length of the result is determined by \code{n} for |
| \code{rgeom}, and is the maximum of the lengths of the |
| numerical arguments for the other functions. |
| |
| The numerical arguments other than \code{n} are recycled to the |
| length of the result. Only the first elements of the logical |
| arguments are used. |
| |
| \code{rgeom} returns a vector of type \link{integer}: if generated |
| values exceed the maximum representable integer they are returned as |
| \code{NA} and a warning is given. |
| } |
| \source{ |
| \code{dgeom} computes via \code{dbinom}, using code contributed by |
| Catherine Loader (see \code{\link{dbinom}}). |
| |
| \code{pgeom} and \code{qgeom} are based on the closed-form formulae. |
| |
| \code{rgeom} uses the derivation as an exponential mixture of Poissons, see |
| |
| Devroye, L. (1986) \emph{Non-Uniform Random Variate Generation.} |
| Springer-Verlag, New York. Page 480. |
| } |
| \seealso{ |
| \link{Distributions} for other standard distributions, including |
| \code{\link{dnbinom}} for the negative binomial which generalizes |
| the geometric distribution. |
| } |
| \examples{ |
| qgeom((1:9)/10, prob = .2) |
| Ni <- rgeom(20, prob = 1/4); table(factor(Ni, 0:max(Ni))) |
| } |
| \keyword{distribution} |