\Header{Lognormal}{The Log Normal Distribution}
\alias{dlnorm}{Lognormal}
\alias{plnorm}{Lognormal}
\alias{qlnorm}{Lognormal}
\alias{rlnorm}{Lognormal}
\keyword{distribution}{Lognormal}
\begin{Usage}
\begin{verbatim}
dlnorm(x, meanlog = 0, sdlog = 1)
plnorm(q, meanlog = 0, sdlog = 1)
qlnorm(p, meanlog = 0, sdlog = 1)
rlnorm(n, meanlog = 0, sdlog = 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{meanlog,sdlog}] mean and standard deviation of the distribution
on the log scale
\end{ldescription}
\end{Arguments}
\begin{Description}
These functions provide information about the log normal distribution
whose logarithm has mean equal to \texttt{meanlog} and standard
deviation equal to \texttt{sdlog}.  \texttt{dlnorm} gives the density,
\texttt{plnorm} gives the distribution function \texttt{qlnorm} gives the
quantile function and \texttt{rlnorm} generates random deviates.

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

The log normal distribution has density
\deqn{
f(x) = \frac{1}{\sqrt{2\pi}\sigma x} e^{-(\log(x) - \mu)^2/2 \sigma^2}
}{f(x) = 1/(sqrt(2 pi) sigma x) e^-((log x - mu)^2 / (2 sigma^2))}
where \eqn{\mu}{} and \eqn{\sigma}{} are the mean and standard
deviation of the logarithm.\end{Description}
\begin{SeeAlso}
\texttt{\Link{dnorm}} for the normal distribution.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
dlnorm(1) == dnorm(0)
x <- rlnorm(1000)	# not yet always :
all(abs(x  -  qlnorm(plnorm(x))) < 1e4 * .Machine$double.eps * x)
\end{ExampleCode}
\end{Examples}

