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Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties

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  • Vilca, Filidor
  • Balakrishnan, N.
  • Zeller, Camila Borelli

Abstract

The Generalized Inverse Gaussian (GIG) distribution has found many interesting applications; see Jørgensen [24]. This rich family includes some well-known distributions, such as the inverse Gaussian, gamma and exponential, as special cases. These distributions have been used as the mixing density for building some heavy-tailed multivariate distributions including the normal inverse Gaussian, Student-t and Laplace distributions. In this paper, we use the GIG distribution in the context of the scale-mixture of skew-normal distributions, deriving a new family of distributions called Skew-Normal Generalized Hyperbolic distributions. This new flexible family of distributions possesses skewness with heavy-tails, and generalizes the symmetric normal inverse Gaussian and symmetric generalized hyperbolic distributions.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:128:y:2014:i:c:p:73-85
    DOI: 10.1016/j.jmva.2014.03.002
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    3. Marcel Wollschlager & Rudi Schafer, 2015. "Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returns," Papers 1506.08054, arXiv.org.
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    5. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2021. "A formulation for continuous mixtures of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    6. Arellano-Valle, Reinaldo B. & Ferreira, Clécio S. & Genton, Marc G., 2018. "Scale and shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 98-110.

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