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))

[Package sn version 0.33 Index]