Statistics and Computing

, Volume 29, Issue 3, pp 415–428 | Cite as

Robust finite mixture modeling of multivariate unrestricted skew-normal generalized hyperbolic distributions

  • Mohsen Maleki
  • Darren WraithEmail author
  • Reinaldo B. Arellano-Valle


In this paper, we introduce an unrestricted skew-normal generalized hyperbolic (SUNGH) distribution for use in finite mixture modeling or clustering problems. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families such as the scale mixtures of skew-normal, the skew-normal generalized hyperbolic and its corresponding symmetric versions. The class of distributions provides a much needed unified framework where the choice of the best fitting distribution can proceed quite naturally through either parameter estimation or by placing constraints on specific parameters and assessing through model choice criteria. The class has several desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. We illustrate the flexibility of the proposed class of distributions in a mixture modeling context using a Bayesian framework and assess the performance using simulated and real data.


Bayesian analysis Finite mixtures MCMC Unrestricted skew-normal generalized hyperbolic family Skew-normal Generalized hyperbolic distribution 



The authors would like to thank the coordinating editor and anonymous reviewers for their suggestions, corrections and encouragement, which helped us to improve earlier versions of the manuscript.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Mohsen Maleki
    • 1
  • Darren Wraith
    • 2
    Email author
  • Reinaldo B. Arellano-Valle
    • 3
  1. 1.Department of StatisticsShiraz UniversityShirazIran
  2. 2.Institute of Health and Biomedical Innovation (IHBI)Queensland University of Technology (QUT)BrisbaneAustralia
  3. 3.Department of StatisticsUniversidad Católica de ChileSantiagoChile

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