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Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables
C16 - Specific Distributions
C46 - Specific Distributions; Specific Statistics
Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by non-singular affine transformations of vectors of independent two-piece normal variables, the most important subclass of Ferreira and Steel’s general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of Arellano-Valle and Azzalini’s unified skew-normal densities and then using the property of closure under marginalization of the latter class.