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Marginal Replacement in Multivariate Densities, with Application to Skewing Spherically Symmetric Distributions

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  • Jones, M. C.

Abstract

We consider a simple general construct, that of marginal replacement in a multivariate distribution, that provides, in particular, an interesting way of producing distributions that have a skew marginal from spherically symmetric starting points. Particular examples include a new multivariate beta distribution and a new multivariate t/skew t distribution, along with Azzalini and colleagues' multivariate skew normal distribution.

Suggested Citation

  • Jones, M. C., 2002. "Marginal Replacement in Multivariate Densities, with Application to Skewing Spherically Symmetric Distributions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 85-99, April.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:85-99
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    References listed on IDEAS

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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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    Cited by:

    1. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, University Library of Munich, Germany.
    2. Uesu, Kagumi & Shimizu, Kunio & SenGupta, Ashis, 2015. "A possibly asymmetric multivariate generalization of the Möbius distribution for directional data," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 146-162.
    3. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, University Library of Munich, Germany.
    4. Balaev , Alexey, 2011. "Multivariate skewed t-distribution with degrees of freedom vector and its application to financial modeling," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 23(3), pages 79-97.
    5. Nott, David J. & Fielding, Mark & Leonte, Daniela, 2009. "On a generalization of the Laplace approximation," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1397-1403, June.
    6. C. Adcock, 2010. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution," Annals of Operations Research, Springer, vol. 176(1), pages 221-234, April.

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