Quantities related to the 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.

Description

Computes mean vector, variance matrix and other relevant quantities of a given multivariate skew-normal distribution.

Details

The meaning of the parameters is explained in the references below, especially Azzalini and Capitanio (1998).

Value

a list containing the following components

xi, as given on input
omega vector of scale parameters
mean numeric vector representing the mean value of the distribution
variance variance matrix of the distribution
Omega_con,Omega_conc correlation matrix and concentration matrix associated to Omega
Psi covariance matrix of the equivalent (lambda,Psi) parametrization
lambda, shape parameters of the marginal distributions, in two equivalent forms
gamma1 numeric vector with marginal indices of skewness

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, part 3.

See Also

dmsn

Examples

a = msn_quantities([0,0], eye(2), [2,3])


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