Cumulants and distribution of a skew-normal variate after conditioning

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.

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.

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, part 3.

See Also

plot_msn_cond

Examples

Omega = eye(3)+0.5.*ones(3,3)
a = msn_conditional(zeros(1,3), Omega, [1:3], 3, -0.75)


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