\Header{Weibull}{The Weibull Distribution}
\alias{dweibull}{Weibull}
\alias{pweibull}{Weibull}
\alias{qweibull}{Weibull}
\alias{rweibull}{Weibull}
\keyword{distribution}{Weibull}
\begin{Description}\relax
Density, distribution function, quantile function and random
generation for the Weibull distribution with parameters \code{shape}
and \code{scale}.\end{Description}
\begin{Usage}
\begin{verbatim}
dweibull(x, shape, scale = 1, log = FALSE)
pweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
qweibull(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
rweibull(n, shape, scale = 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 to generate.
\item[\code{shape, scale}] shape and scale parameters.
\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{scale} is omitted it assumes the default value of \code{1}.

The Weibull distribution with \code{shape} parameter \eqn{a}{} and
\code{scale} parameter \eqn{b}{} has density given by
\deqn{f(x) = (a/b) {(x/b)}^{a-1} \exp (-{(x/b)}^{a})}{f(x) = (a/b) (x/b)^(a-1) exp(- (x/b)^a)}
for \eqn{x > 0}{}.\end{Details}
\begin{Value}
\code{dweibull} gives the density,
\code{pweibull} gives the distribution function,
\code{qweibull} gives the quantile function, and
\code{rweibull} 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{-pweibull(t, r, lower = FALSE, log = TRUE)}.\end{Note}
\begin{SeeAlso}\relax
\code{\Link{dexp}} for the Exponential which is a special case of a
Weibull distribution.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
x <- 1:10
all.equal(dweibull(x, shape = 1), dexp(x))
all.equal(pweibull(x, shape = 1, scale = pi), pexp(x, rate = 1/pi))
all.equal(qweibull(x/11, shape = 1, scale = pi), qexp(x/11, rate = 1/pi))
\end{ExampleCode}
\end{Examples}

