\Header{Cauchy}{The Cauchy Distribution}
\alias{dcauchy}{Cauchy}
\alias{pcauchy}{Cauchy}
\alias{qcauchy}{Cauchy}
\alias{rcauchy}{Cauchy}
\keyword{distribution}{Cauchy}
\begin{Description}\relax
Density, distribution function, quantile function and random
generation for the Cauchy distribution with location parameter
\code{location} and scale parameter \code{scale}.\end{Description}
\begin{Usage}
\begin{verbatim}
dcauchy(x, location = 0, scale = 1, log = FALSE)
pcauchy(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qcauchy(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rcauchy(n, location = 0, 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{location, scale}] location 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{location} or \code{scale} are not specified, they assume
the default values of \code{0} and \code{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{Details}
\begin{Value}
\code{dcauchy}, \code{pcauchy}, and \code{qcauchy} are respectively
the density, distribution function and quantile function of the Cauchy
distribution.  \code{rcauchy} generates random deviates from the
Cauchy.\end{Value}
\begin{SeeAlso}\relax
\code{\Link{dt}} for the t distribution which generalizes
\code{dcauchy(*, l = 0, s = 1)}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
all.equal(dcauchy(-1:4), 1 / (pi*(1 + (-1:4)^2)))
\end{ExampleCode}
\end{Examples}

