\Header{NChisquare}{The Non-Central Chi-Square Distribution}
\alias{dnchisq}{NChisquare}
\alias{pnchisq}{NChisquare}
\alias{qnchisq}{NChisquare}
\alias{rnchisq}{NChisquare}
\keyword{distribution}{NChisquare}
\begin{Usage}
\begin{verbatim}
--- these are DEPRECATED, use  Xchisq( . , df, ncp) instead ---

dnchisq(x, df, lambda)
pnchisq(q, df, lambda)
qnchisq(p, df, lambda)
rnchisq(n, df, lambda)
\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{df,lambda}] degrees of freedom and non-centrality parameter.
\end{ldescription}
\end{Arguments}
\begin{Description}
--- these are DEPRECATED, use  Xchisq( . , df, ncp) instead ---

These functions provide information about the non-central chi-square
distribution with \texttt{df} degrees of freedom and non-centrality
parameter \texttt{lambda}.  \texttt{dnchisq} gives the density,
\texttt{pnchisq} gives the distribution function, \texttt{qnchisq} gives
the quantile function and \texttt{rnchisq} generates random deviates.

The non-central chi-square distribution with \eqn{df}{} degrees of
freedom and non-centrality parameter \eqn{\lambda}{} has density
\deqn{
f(x) = e^{-\lambda / 2}
\sum_{r=0}^\infty \frac{\lambda^r}{2^r r!}
\, \mathrm{pchisq}(x, df + 2r)}{f(x) = exp(-lambda/2) SUM_{r=0}^infty (lambda^r / 2^r r!)
pchisq(x, df + 2r)}
for \eqn{x \ge 0}{}.\end{Description}
\begin{SeeAlso}
\texttt{\Link{dchisq}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
pnchisq(1, df = 3, lambda = 0) == pchisq(1, df = 3)
pnchisq(1, df = 3, lambda = 0:4)
\end{ExampleCode}
\end{Examples}

