\HeaderA{ppoints}{Ordinates for Probability Plotting}{ppoints}
\keyword{dplot}{ppoints}
\keyword{arith}{ppoints}
\keyword{distribution}{ppoints}
\begin{Description}\relax
Generates the sequence of \dQuote{probability} points
\code{(1:m - a)/(m + (1-a)-a)}
where \code{m} is either \code{n}, if \code{length(n)==1}, or
\code{length(n)}.
\end{Description}
\begin{Usage}
\begin{verbatim}
ppoints(n, a = ifelse(n <= 10, 3/8, 1/2))
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{n}] either the number of points generated or a vector of
observations.
\item[\code{a}] the offset fraction to be used; typically in \eqn{(0,1)}{}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
If \eqn{0 < a < 1}{}, the resulting values are within \eqn{(0,1)}{}
(excluding boundaries).
In any case, the resulting sequence is symmetric in \eqn{[0,1]}{}, i.e.,
\code{p + rev(p) == 1}.

\code{ppoints()} is used in \code{qqplot} and \code{qqnorm} to generate
the set of probabilities at which to evaluate the inverse distribution.

The choice of \code{a} follows the documentation of the function of the
same name in Becker \emph{et al} (1988), and appears to have been
motivated by results from Blom (1958) on approximations to expect normal
order statistics (see also \code{\LinkA{quantile}{quantile}}).
\end{Details}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.

Blom, G. (1958)
\emph{Statistical Estimates and Transformed Beta Variables.}
Wiley
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{qqplot}{qqplot}}, \code{\LinkA{qqnorm}{qqnorm}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
ppoints(4) # the same as  ppoints(1:4)
ppoints(10)
ppoints(10, a=1/2)
\end{ExampleCode}
\end{Examples}

