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Series form of the characteristic functions of scale mixtures of multivariate skew-normal distributions

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  • Kim, SungBum
  • Kim, Hyoung-Moon

Abstract

Based on two series representations of the error function and a series representation of the Faddeeva function, the characteristic functions of scale mixtures of skew-normal distributions in univariate and multivariate cases are derived in series form instead of the previously suggested two-dimensional integral form without using contour integration. This is accomplished by applying the Lebesgue dominated convergence theorem to change the order of integral and limit. After integrating out each mixing variable, the series representation is expressed as in closed-form. Series form greatly reduces the computing times compared to the integral form, which is visualized via parallel box plots in a skew-t and a skew-slash distributions and a result of application on goodness-of-fit test.

Suggested Citation

  • Kim, SungBum & Kim, Hyoung-Moon, 2022. "Series form of the characteristic functions of scale mixtures of multivariate skew-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 172-187.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:172-187
    DOI: 10.1016/j.matcom.2022.02.033
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    References listed on IDEAS

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    1. S. T. Boris Choy & Adrian F. M. Smith, 1997. "On Robust Analysis of a Normal Location Parameter," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 463-474.
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    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. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    5. Emrah Altun & Huseyin Tatlidil & Gamze Ozel, 2019. "Value-at-risk estimation with new skew extension of generalized normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3663-3681, July.
    6. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    7. 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.
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    Cited by:

    1. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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