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Characteristic functions of scale mixtures of multivariate skew-normal distributions


  • Kim, Hyoung-Moon
  • Genton, Marc G.


We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew-normal distributions. In particular, we describe the characteristic function of skew-normal, skew-t, and other related distributions.

Suggested Citation

  • Kim, Hyoung-Moon & Genton, Marc G., 2011. "Characteristic functions of scale mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1105-1117, August.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:7:p:1105-1117

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    References listed on IDEAS

    1. Reinaldo Arellano-Valle & Marc Genton, 2010. "An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 363-381, April.
    2. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    3. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew-"t" and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    4. Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew-normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574.
    5. 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.
    6. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    7. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
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    Cited by:

    1. Otiniano, C.E.G. & Rathie, P.N. & Ozelim, L.C.S.M., 2015. "On the identifiability of finite mixture of Skew-Normal and Skew-t distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 103-108.
    2. S. Rao Jammalamadaka & Tomasz J. Kozubowski, 2017. "A General Approach for Obtaining Wrapped Circular Distributions via Mixtures," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 133-157, February.
    3. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    4. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
    5. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.
    6. Adcock, C.J., 2014. "Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution," European Journal of Operational Research, Elsevier, vol. 234(2), pages 392-401.


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