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\name{qmvnorm}
\alias{qmvnorm}
\title{ Quantiles of the Multivariate Normal Distribution }
\description{
Computes the equicoordinate quantile function of the multivariate normal
distribution for arbitrary correlation matrices
based on an inversion of the algorithms by Genz and Bretz.
}
\usage{
qmvnorm(p, interval = c(-10, 10), tail = c("lower.tail",
"upper.tail", "both.tails"), mean = 0, corr = NULL,
sigma = NULL, algorithm = GenzBretz(), ...)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{p}{ probability.}
\item{interval}{ a vector containing the end-points of the interval to be
searched by \code{\link{uniroot}}.}
\item{tail}{ specifies which quantiles should be computed.
\code{lower.tail} gives the quantile \eqn{x} for which
\eqn{P[X \le x] = p}, \code{upper.tail} gives \eqn{x} with
\eqn{P[X > x] = p} and
\code{both.tails} leads to \eqn{x}
with \eqn{P[-x \le X \le x] = p}.}
\item{mean}{ the mean vector of length n. }
\item{corr}{ the correlation matrix of dimension n.}
\item{sigma}{ the covariance matrix of dimension n. Either \code{corr} or
\code{sigma} can be specified. If \code{sigma} is given, the
problem is standardized. If neither \code{corr} nor
\code{sigma} is given, the identity matrix is used
for \code{sigma}. }
\item{algorithm}{ an object of class \code{\link{GenzBretz}} or \code{\link{Miwa}}
specifying both the algorithm to be used as well as
the associated hyper parameters.}
\item{...}{ additional parameters to be passed to
\code{\link{uniroot}}.}
}
\details{
Only equicoordinate quantiles are computed, i.e., the quantiles in each
dimension coincide. Currently, the distribution function is inverted by
using the
\code{\link{uniroot}} function which may result in limited accuracy of the
quantiles.
}
\value{
A list with four components: \code{quantile} and \code{f.quantile}
give the location of the quantile and the value of the function
evaluated at that point. \code{iter} and \code{estim.prec} give the number
of iterations used and an approximate estimated precision from
\code{\link{uniroot}}.
}
\seealso{\code{\link{pmvnorm}}, \code{\link{qmvt}}}
\examples{
qmvnorm(0.95, sigma = diag(2), tail = "both")
}
\keyword{distribution}
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