A multivariate modified skew-normal distribution

Sagnik Mondal*, Reinaldo B. Arellano-Valle, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a multivariate version of the modified skew-normal distribution, which contains the multivariate normal distribution as a special case. Unlike the Azzalini multivariate skew-normal distribution, this new distribution has a nonsingular Fisher information matrix when the skewness parameters are all zero, and its profile log-likelihood of the skewness parameters is always a non-monotonic function. We study some basic properties of the proposed family of distributions and present an expectation-maximization (EM) algorithm for parameter estimation that we validate through simulation studies. Finally, we apply the proposed model to the univariate frontier data and to a trivariate wind speed data, and compare its performance with the Azzalini skew-normal model.

Original languageEnglish (US)
Pages (from-to)511-555
Number of pages45
JournalStatistical Papers
Issue number2
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • EM algorithm
  • Fisher information matrix
  • Modified skew-normal
  • Skew-elliptical
  • Skew-generalized normal
  • Skew-normal

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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