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Gram–Charlier-like expansions of power-raised hyperbolic secant laws

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  • Faliva, Mario
  • Quatto, Piero
  • Zoia, Maria Grazia

Abstract

Spherical distributions arise quite naturally as multivariate versions of univariate (even) densities and prove useful in several applications. Likewise their univariate counterparts, they may not always meet the kurtosis requirements of empirical evidence. This paper devises a methodological approach which duly reshapes spherical distributions to match kurtosis requirements to due extent. This approach is tailored to the family of power-raised hyperbolic secant laws and hinges on Gram–Charlier-like expansions via second-degree orthogonal polynomials.

Suggested Citation

  • Faliva, Mario & Quatto, Piero & Zoia, Maria Grazia, 2018. "Gram–Charlier-like expansions of power-raised hyperbolic secant laws," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 229-234.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:229-234
    DOI: 10.1016/j.spl.2018.01.027
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    References listed on IDEAS

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    1. Zografos, K., 2008. "On Mardia's and Song's measures of kurtosis in elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 858-879, May.
    2. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Maria Grazia Zoia & Gianmarco Vacca & Laura Barbieri, 2020. "Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions," Risks, MDPI, vol. 8(4), pages 1-21, November.

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