\HeaderA{Exponential}{The Exponential Distribution}{Exponential}
\aliasA{dexp}{Exponential}{dexp}
\aliasA{pexp}{Exponential}{pexp}
\aliasA{qexp}{Exponential}{qexp}
\aliasA{rexp}{Exponential}{rexp}
\keyword{distribution}{Exponential}
\begin{Description}\relax
Density, distribution function, quantile function and random
generation for the exponential distribution with rate \code{rate}
(i.e., mean \code{1/rate}).
\end{Description}
\begin{Usage}
\begin{verbatim}
dexp(x, rate = 1, log = FALSE)
pexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)
qexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE)
rexp(n, rate = 1)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x, q}] vector of quantiles.
\item[\code{p}] vector of probabilities.
\item[\code{n}] number of observations. If \code{length(n) > 1}, the length
is taken to be the number required.
\item[\code{rate}] vector of rates.
\item[\code{log, log.p}] logical; if TRUE, probabilities p are given as log(p).
\item[\code{lower.tail}] logical; if TRUE (default), probabilities are
\eqn{P[X \le x]}{P[X <= x]}, otherwise, \eqn{P[X > x]}{P[X > x]}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
If \code{rate} is not specified, it assumes the default value of
\code{1}.

The exponential distribution with rate \eqn{\lambda}{} has density
\deqn{
f(x) = \lambda {e}^{- \lambda x}}{f(x) = lambda e^(- lambda x)}
for \eqn{x \ge 0}{}.
\end{Details}
\begin{Value}
\code{dexp} gives the density,
\code{pexp} gives the distribution function,
\code{qexp} gives the quantile function, and
\code{rexp} generates random deviates.
\end{Value}
\begin{Note}\relax
The cumulative hazard \eqn{H(t) = - \log(1 - F(t))}{H(t) = - log(1 - F(t))}
is \code{-pexp(t, r, lower = FALSE, log = TRUE)}.
\end{Note}
\begin{Source}\relax
\code{dexp}, \code{pexp} and \code{qexp} are all calculated
from numerically stable versions of the definitions.

\code{rexp} uses

Ahrens, J. H. and Dieter, U. (1972).
Computer methods for sampling from the exponential and normal distributions.
\emph{Communications of the ACM}, \bold{15}, 873--882.
\end{Source}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
\emph{Continuous Univariate Distributions}, volume 1, chapter 19.
Wiley, New York.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{exp}{exp}} for the exponential function,
\code{\LinkA{dgamma}{dgamma}} for the gamma distribution and
\code{\LinkA{dweibull}{dweibull}} for the Weibull distribution, both of which
generalize the exponential.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
dexp(1) - exp(-1) #-> 0
\end{ExampleCode}
\end{Examples}

