Marginal distributions of random vectors generated by affine transformations of independent two-piece normal variables. (English) Zbl 1245.62059
Summary: 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 J.T.A.S. Ferreira and M.F.J. Steel’s [Stat. Sin. 17, No. 2, 505–529 (2007; Zbl 1144.62035)] general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of R.B. Arellano-Valle and A. Azzalini’s [Scand. J. Stat. 33, No. 3, 561–574 (2006; Zbl 1117.62051)] unified skew-normal densities and then using the property of closure under marginalization of the latter class.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62H10 | Multivariate distribution of statistics |
References:
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