\Header{Weibull}{The Weibull Distribution}
\alias{dweibull}{Weibull}
\alias{pweibull}{Weibull}
\alias{qweibull}{Weibull}
\alias{rweibull}{Weibull}
\keyword{distribution}{Weibull}
\begin{Usage}
\begin{verbatim}
dweibull(x, shape, scale = 1)
pweibull(q, shape, scale = 1)
qweibull(p, shape, scale = 1)
rweibull(n, shape, scale = 1)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\texttt{x,q}] vector of quantiles.
\item[\texttt{p}] vector of probabilities.
\item[\texttt{n}] number of observations to generate.
\item[\texttt{shape,scale}] shape and scale parameters.
\end{ldescription}
\end{Arguments}
\begin{Description}
These functions provide information about the Weibull distribution
with parameters \texttt{shape} and \texttt{scale}.  \texttt{dweibull} gives
the density, \texttt{pweibull} gives the distribution function,
\texttt{qweibull} gives the quantile function and \texttt{rweibull}
generates random deviates.

If \texttt{scale} is omitted it assumes the default value of \texttt{1}.

The Weibull distribution with \texttt{shape} parameter \eqn{a}{} and
\texttt{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{Description}
\begin{SeeAlso}
\texttt{\Link{dexp}} for the Exponential which is a special case of a
Weibull distribution.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
x <- 1:10
dweibull(x, shape = 1) == dexp(x)
pweibull(x, shape = 1, scale = pi) == pexp(x, rate = 1/pi)
qweibull(x/11, shape = 1, scale = pi) == qexp(x/11, rate = 1/pi)
\end{ExampleCode}
\end{Examples}

