Scale and shape mixtures of multivariate skew-normal distributions

Reinaldo B. Arellano-Valle, Clécio S. Ferreira, Marc G. Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We introduce a broad and flexible class of multivariate distributions obtained by both scale and shape mixtures of multivariate skew-normal distributions. We present the probabilistic properties of this family of distributions in detail and lay down the theoretical foundations for subsequent inference with this model. In particular, we study linear transformations, marginal distributions, selection representations, stochastic representations and hierarchical representations. We also describe an EM-type algorithm for maximum likelihood estimation of the parameters of the model and demonstrate its implementation on a wind dataset. Our family of multivariate distributions unifies and extends many existing models of the literature that can be seen as submodels of our proposal.

Original languageEnglish (US)
Pages (from-to)98-110
Number of pages13
JournalJournal of Multivariate Analysis
StatePublished - Jul 2018

Bibliographical note

Funding Information:
This research was supported by Fondecyt (Chile) 1120121 and 1150325 , by FAPEMIG (Minas Gerais State Foundation for Research Development) grant CEX APQ 01944/17 , and by the King Abdullah University of Science and Technology (KAUST) . We thank the Editor, Associate Editor and four anonymous reviewers for comments that improved the paper. We also thank Prof. Adelchi Azzalini for suggesting Proposition 1 during a seminar presentation of this work at the University of Padova and Prof. Mauricio Castro for some initial discussions on the topic of this paper.

Publisher Copyright:
© 2018 Elsevier Inc.


  • EM-algorithm
  • Scale mixtures of normal distributions
  • Scale mixtures of skew-normal distributions
  • Shape mixtures of skew-normal distributions
  • Skew scale mixtures of normal distributions
  • Skew-normal distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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