msn.quantities: 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.

msn.quantities(xi, Omega, alpha)

numeric vector giving the location parameter, of length k, say. Missing values are not allowed.

Omega

a covariance matrix of size k by k. Missing values are not allowed.

alpha

numeric vector of shape parameter of length k. Missing values are not allowed.

A list containing the following components:
xithe input parameter xi.
Omegathe input parameter Omega.
alphathe input parameter alpha.
omegavector of scale parameters.
meannumeric vector representing the mean value of the distribution.
variancevariance matrix of the distribution.
Omega.convconcentration matrix associated to Omega, i.e. its inverse.
Omega.corcorrelation matrix associated to Omega.
Omega.pcorpartial correlations matrix associated to Omega.
lambdashape parameters of the marginal distributions, in two equivalent forms.
Psicorrelation matrix of the equivalent (lambda,Psi) parametrization.
deltathe parameter delta which determines the shape of the marginal distributions.
skewnessnumeric vector with marginal indices of skewness (the standardised third cumulant).

The meaning of the parameters is explained in the references below, especially Azzalini and Capitanio (1999).

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715--726.

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

Omega <- 5*diag(3)+outer(1:3,1:3)
msn.quantities(c(0,0,1), Omega, c(-2,2,3))

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