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Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables

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  • Maximiano Pinheiro

Abstract

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.

Suggested Citation

  • Maximiano Pinheiro, 2010. "Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables," Working Papers w201013, Banco de Portugal, Economics and Research Department.
  • Handle: RePEc:ptu:wpaper:w201013
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    References listed on IDEAS

    as
    1. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    2. Villani, Mattias & Larsson, Rolf, 2004. "The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis," Working Paper Series 175, Sveriges Riksbank (Central Bank of Sweden).
    3. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
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    More about this item

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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