msn.quantities {sn} | R Documentation |
Computes mean vector, variance matrix and other relevant quantities of a given multivariate skew-normal distribution.
msn.quantities(xi, Omega, alpha)
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.
|
The meaning of the parameters is explained in the references below, especially Azzalini and Capitanio (1999).
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). |
Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715726.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579602.
Omega <- 5*diag(3)+outer(1:3,1:3) msn.quantities(c(0,0,1), Omega, c(-2,2,3))