\Header{Beta}{The Beta Distribution}
\alias{dbeta}{Beta}
\alias{pbeta}{Beta}
\alias{qbeta}{Beta}
\alias{rbeta}{Beta}
\keyword{distribution}{Beta}
\begin{Usage}
\begin{verbatim}
dbeta(x, shape1, shape2, ncp=0)
pbeta(q, shape1, shape2, ncp=0)
qbeta(p, shape1, shape2)
rbeta(n, shape1, shape2)
\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{shape1,shape2}] positive parameters of the beta distribution.
\item[\texttt{ncp}] non-centrality parameter.
\end{ldescription}
\end{Arguments}
\begin{Value}
These functions provide information about the Beta distribution
with parameters \texttt{shape1} and \texttt{shape2} (and optional non-centrality
parameter \texttt{ncp}).  \texttt{dbeta} gives the density,
\texttt{pbeta} the distribution function, \texttt{qbeta} the
quantile function and \texttt{rbeta} generates random deviates.

The Beta distribution with parameters \texttt{shape1} \eqn{= a}{} and \texttt{shape2}
\eqn{= b}{} has density
\deqn{f(x)=\frac{\Gamma (a + b )}{\Gamma (a) \Gamma (b)}{x}^{a} {(1-x)}^{b}
}{Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1)}
for \eqn{a > 0}{}, \eqn{b > 0}{} and \eqn{0 < x < 1}{}.\end{Value}
\begin{SeeAlso}
\texttt{\Link{beta}} for the beta function, and \texttt{\Link{dgamma}} for the
Gamma distribution.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
x <- seq(0,1, length=21)
dbeta(x, 1, 1)
pbeta(x, 1, 1)
\end{ExampleCode}
\end{Examples}

