msn.conditional {sn}R Documentation

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

Details

See the reference below for details and background.

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.

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)

[Package sn version 0.4-4 Index]