sn (version 0.4-3)

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.

Usage

msn.quantities(xi=rep(0,length(alpha)), Omega, alpha)
msn.quantities(dp= )

Arguments

xi

numeric vector giving the location parameter, of length d, say. Missing values are not allowed.

Omega

a covariance matrix of size d by d. Missing values are not allowed.

alpha

numeric vector of shape parameter of length d. Missing values are not allowed.

dp

a list with three components named xi, Omega, alpha, containing quantities as described above. If dp is set, then the component parameters must not be.

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
  the mean value of the distribution (vector)
• variance
  variance-covariance 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
• Psi
  correlation matrix of the equivalent (lambda,Psi) parametrization.
• delta
  the parameter delta which determines the shape of the marginal distributions; this is related to lambda
• skewness
  numeric vector with marginal indices of skewness (the standardised third cumulant).

synopsis

msn.quantities(xi=rep(0,length(alpha)), Omega, alpha, dp = NULL)

Details

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

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))