sn (version 0.33)

msn.conditional: Cumulants and distribution of a skew-normal variate after conditioning

Description

Finds cumulants up to 3rd order of a multivariate skew-normal distribution conditionally on the values taken on by some of its components, and finds a multivariate skew-normal distribution with the same cumulants.

Usage

msn.conditional(xi, Omega, alpha, fixed.comp, fixed.values)

Arguments

xi

a numeric vector of length k, say, giving the location parameter.

Omega

a covariance matrix of dimension (k,k).

alpha

a numeric vector of length k, which regulates the shape of the density.

fixed.comp

a vector containing a subset of 1:k which selects the components whose values are to be fixed; it must be of length k-2.

fixed.values

a numeric vector of values taken on by the components fixed.comp; it must be of the same length of fixed.comp.

Value

• A list containing the following elements:
• cumulants
  a list containing mean vector, variance matrix, and indices of skewness of the conditional distribution.
• fit
  a list containing the parameters of the fitted skew-normal distribution in the (xi,Omega,alpha) parametrization, plus the vector delta.

Details

See the reference below for details and background.

References

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

See Also

msn.cond.plot, msn.marginal

Examples

Omega <- diag(3)+0.5*outer(rep(1,3),rep(1,3))
a<- msn.conditional(rep(0,3), Omega, 1:3, 3, -0.75)