msn.quantities {sn}R Documentation

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

xi 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.

Details

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

Value

a list containing the following components

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

References

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.

See Also

dmsn

Examples

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