sn (version 0.4-3)

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)
msn.conditional(dp=, fixed.comp, fixed.values)

Arguments

xi

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

Omega

a covariance matrix of dimension (d,d).

alpha

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

fixed.comp

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

dp

a list containing the components xi, Omega, alpha, contaning quantities as described above

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.

synopsis

msn.conditional(xi = rep(0, length(alpha)), Omega, alpha, fixed.comp, fixed.values, dp = NULL)

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)