Marginal distributions of random vectors generated by affine transformations of independent two-piece normal variables

Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by nonsingular 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. © 2012 maximiano pinheiro.