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\name{mtrunct}
\alias{dmtrunct}
\alias{pmtrunct}
\title{The multivariate truncated Student's \emph{t} distribution}
\description{
The probability density function and the distribution function of the
multivariate truncated Student's \emph{t} distribution
}
\usage{
dmtrunct(x, mean, S, df, lower, upper, log = FALSE, ...)
pmtrunct(x, mean, S, df, lower, upper, ...)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{x}{ either a vector of length \code{d}
or a matrix with \code{d} columns, where \code{d=ncol(S)}, giving
the coordinates of the point(s) where the density must be evaluated. }
\item{mean}{either a vector of length \code{d}, representing the location
parameter (equal to the mean vector when \code{df>1}) of the pre-truncation
distribution or a matrix whose rows represent different mean vectors;
in the matrix case, its dimensions must match those of \code{x}.}
\item{S}{a symmetric positive-definite matrix representing the
scale matrix, such that \code{S*df/(df-2)} is the variance-covariance
matrix of the pre-truncation distribution when \code{df>2}.}
\item{df}{degrees of freedom; it must be a positive integer}
\item{lower}{a vector representing the lower truncation values of the
component variables; \code{-Inf} values are allowed.
If missing, it is set equal to \code{rep(-Inf, d)}.}
\item{upper}{a vector representing the upper truncation values of the
component variables; \code{Inf} values are allowed.
If missing, it is set equal to \code{rep(Inf, d)}.}
\item{log}{a logical value (default value is \code{FALSE});
if \code{TRUE}, the logarithm of the density is computed.}
\item{\dots}{arguments passed to \code{sadmvt},
among \code{maxpts}, \code{absrel}, \code{releps}.}
}
\details{The dimension \code{d} cannot exceed \code{20}.}
\value{a numeric vector}
% \references{%% ~put references to the literature/web site here ~}
\author{Adelchi Azzalini}
% \note{%% ~~further notes~~}
\seealso{ \code{\link{sadmvt}} for regulating accuracy}
\examples{
m2 <- c(0.5, -1)
V2 <- matrix(c(1.5, -1.75, -1.75, 3), 2, 2)
lower <- a <- c(-1, -2.5)
upper <- b <- c(2, 1)
set.seed(1)
points <- matrix(runif(10, -3, 3), nrow=5, ncol=2)
pdf <- dmtrunct(points, mean=m2, S=V2, df=4, lower, upper)
cdf <- pmtrunct(points, mean=m2, S=V2, df=4, lower, upper)
}
%----
\keyword{distribution}
\keyword{multivariate}
\concept{multivariate truncated t distribution}
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