\name{msn.quantities}
\alias{msn.quantities}
\title{
Quantities related to the multivariate skew-normal distribution.
}
\description{
Computes mean vector, variance matrix and other relevant quantities
of a given multivariate skew-normal distribution.
}
\usage{
msn.quantities(xi, Omega, alpha)
}
\arguments{
\item{xi}{
numeric vector giving the location parameter, of length \code{k}, say.
Missing values are not allowed.
}
\item{Omega}{
a covariance matrix of size \code{k} by \code{k}.
Missing values are not allowed.
}
\item{alpha}{
numeric vector of shape parameter of length \code{k}.
Missing values are not allowed.
}}
\value{
a list containing the following components

\item{xi}{
the input parameter \code{xi}
}
\item{Omega}{
the input parameter  \code{Omega}
}
\item{alpha}{
the input parameter  \code{alpha}
}
\item{omega}{
vector of scale parameters
}
\item{mean}{
numeric vector representing the mean value of the distribution
}
\item{variance}{
variance matrix of the distribution
}
\item{Omega.conv}{
concentration matrix associated to \code{Omega}, i.e. its inverse
}
\item{Omega.cor}{
correlation matrix associated to \code{Omega}
}
\item{Omega.pcor}{
partial correlations matrix associated to \code{Omega}
}
\item{lambda}{
shape parameters of the marginal distributions, in two equivalent
forms
}
\item{Psi}{
correlation matrix of the equivalent \code{(lambda,Psi)} parametrization
}
\item{delta}{
the parameter \code{delta} which determines the shape of the marginal 
distributions
}

\item{skewness}{
numeric vector with marginal indices of skewness (the standardised
third cumulant)
}}
\details{
The meaning of the parameters is explained in the references below,
especially Azzalini and Capitanio (1999).
}
\references{
Azzalini, A. and Dalla Valle, A. (1996).
The multivariate skew-normal distribution.
\emph{Biometrika}
\bold{83}, 715--726.


Azzalini, A. and Capitanio, A. (1999).
Statistical applications of the multivariate skew-normal distribution.
\emph{J.Roy.Statist.Soc. B}
\bold{61}, 579--602.
}
\seealso{
\code{\link{dmsn}}
}
\examples{
Omega <- 5*diag(3)+outer(1:3,1:3)
msn.quantities(c(0,0,1), Omega, c(-2,2,3))
}
\keyword{multivariate}
\keyword{distribution}
% Converted by Sd2Rd version 0.3-3.