\name{NoncenHypergeom}\alias{NoncenHypergeom}\alias{rnoncenhypergeom}\alias{dnoncenhypergeom}\title{The Noncentral Hypergeometric Distribution}\description{  Evaluates the density at a single point or all points, and generate random   draws from the Noncentral Hypergeometric distribution.}\usage{dnoncenhypergeom(x=NA, n1, n2, m1, psi)rnoncenhypergeom(n, n1, n2, m1, psi)}\arguments{  \item{x}{The location to evaluate the density.  If \code{x} is NA,    then a matrix is returned with the density evaluated at all possible    points.}  \item{n}{The number of draws to make from the distribution.}  \item{n1}{The size of group one.}  \item{n2}{The size of group two.}  \item{m1}{The observed number of positive outcomes (in both groups).}  \item{psi}{Odds ratio.}}\value{  \code{dnoncenhypergeom} evaluates the density at point \code{x},  or a matrix with  the first column containing the possible values of the random  variable, and the second column containing the probabilities.  \code{rnoncenhypergeom} returns a list of \code{n} random draws from  the distribution.}\details{  The Noncentral Hypergeometric is particularly useful for conditional  inference for \eqn{(2 \times 2)}{(2 x 2)} tables.  We use the  parameterization and algorithms of Liao and Rosen (2001).  The  underlying R code is based on their published code.  See their  article for details of the parameterization.}\source{  J. G. Liao and Ori Rosen. 2001. ``Fast and Stable Algorithms for Computing  and Sampling From the Noncentral Hypergeometric Distribution." \emph{The  American Statistician.} 55: 366-369.}\examples{  density <- dnoncenhypergeom(NA, 500, 500, 500, 6.0)  draws <- rnoncenhypergeom(10, 500, 500, 500, 6.0)}\keyword{distribution}