\Header{Normal}{The Normal Distribution}
\alias{dnorm}{Normal}
\alias{pnorm}{Normal}
\alias{qnorm}{Normal}
\alias{rnorm}{Normal}
\keyword{distribution}{Normal}
\begin{Usage}
\begin{verbatim}
dnorm(x, mean=0, sd=1)
pnorm(q, mean=0, sd=1)
qnorm(p, mean=0, sd=1)
rnorm(n, mean=0, sd=1)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\texttt{x,q}] vector of quantiles.
\item[\texttt{p}] vector of probabilites.
\item[\texttt{n}] number of observations.
\item[\texttt{mean}] vector of means.
\item[\texttt{sd}] vector of standard deviations.
\end{ldescription}
\end{Arguments}
\begin{Description}
These functions provide information about the normal distribution with
mean equal to \texttt{mean} and standard deviation equal to \texttt{sd}.
\texttt{dnorm} gives the density, \texttt{pnorm} gives the distribution
function \texttt{qnorm} gives the quantile function and \texttt{rnorm}
generates random deviates.

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

The normal distribution has density
\deqn{
f(x) =
\frac{1}{\sqrt{2\pi}\sigma} e^{-(x-\mu)^2/2\sigma^2}}{f(x) = 1/(sqrt(2 pi) sigma) e^-((x - mu)^2/(2 sigma^2))
}
where \eqn{\mu}{mu} is the mean of the distribution and
\eqn{\sigma}{sigma} the standard deviation.\end{Description}
\begin{SeeAlso}
\texttt{\Link{runif}} and \texttt{\Link{.Random.seed}} about random number
generation, and \texttt{\Link{dlnorm}} for the \emph{Log}normal distribution.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
dnorm(0) == 1/ sqrt(2*pi)
dnorm(1) == exp(-1/2)/ sqrt(2*pi)
dnorm(1) == 1/ sqrt(2*pi*exp(1))
\end{ExampleCode}
\end{Examples}

