\Header{Cauchy}{The Cauchy Distribution}
\alias{dcauchy}{Cauchy}
\alias{pcauchy}{Cauchy}
\alias{qcauchy}{Cauchy}
\alias{rcauchy}{Cauchy}
\keyword{distribution}{Cauchy}
\begin{Usage}
\begin{verbatim}
dcauchy(x, location = 0, scale = 1)
pcauchy(q, location = 0, scale = 1)
qcauchy(p, location = 0, scale = 1)
rcauchy(n, location = 0, 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{location,scale}] location and scale parameters.
\end{ldescription}
\end{Arguments}
\begin{Value}
These functions provide information about the Cauchy distribution with
location parameter \texttt{location} and scale parameter \texttt{scale}.

\texttt{dcauchy}, \texttt{pcauchy}, and \texttt{qcauchy} are respectively
the density, distribution function and quantile function of the Cauchy
distribution.  \texttt{rcauchy} generates random deviates from the
Cauchy.

If \texttt{location} or \texttt{scale} are not specified, they assume
the default values of \texttt{0} and \texttt{1} respectively.

The Cauchy distribution with location \eqn{l}{} and scale \eqn{s}{} has
density
\deqn{f(x) = \frac{1}{\pi s}
\left( 1 + \left(\frac{x - l}{s}\right)^2 \right)^{-1}
}{f(x) = 1 / (pi s (1 + ((x-l)/s)^2))}
for all \eqn{x}{}.\end{Value}
\begin{SeeAlso}
\texttt{\Link{dt}} for the t distribution which generalizes
\texttt{dcauchy(*, l = 0, s = 1)}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
dcauchy(-1:4) == 1 / (pi*(1 + (-1:4)^2))
\end{ExampleCode}
\end{Examples}

