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))

Run the code above in your browser using DataLab