\Header{Logistic}{The Logistic Distribution}
\alias{dlogis}{Logistic}
\alias{plogis}{Logistic}
\alias{qlogis}{Logistic}
\alias{rlogis}{Logistic}
\keyword{distribution}{Logistic}
\begin{Usage}
\begin{verbatim}
dlogis(x, location=0, scale=1)
plogis(q, location=0, scale=1)
qlogis(p, location=0, scale=1)
rlogis(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{Description}
These functions provide information about the logistic distribution
with parameters \texttt{location} and \texttt{scale}.  \texttt{dlogis} gives
the density, \texttt{plogis} gives the distribution function
\texttt{qlogis} gives the quantile function and \texttt{rlogis} generates
random deviates.

If \texttt{location} or \texttt{scale} are omitted, they assume the
default values of \texttt{0} and \texttt{1} respectively.

The Logistic distribution with \texttt{location} \eqn{= a}{} and
\texttt{scale} \eqn{= b}{} has density
\deqn{
f(x) = \frac{1}{b} \frac{e^{(x-a)/b}}{(1 + e^{(x-a)/b})^2}
}{f(x) = 1/b exp((x-a)/b) (1 + exp((x-a)/b))^-2.}\end{Description}
\begin{Examples}
\begin{ExampleCode}
x <- 0:4
paste(dlogis(x, loc = 0)) == paste(exp(x) * (1 + exp(x))^-2)
\end{ExampleCode}
\end{Examples}

