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A multivariate modified skew-normal distribution

Author

Listed:
  • Sagnik Mondal

    (King Abdullah University of Science and Technology)

  • Reinaldo B. Arellano-Valle

    (Pontificia Universidad Católica de Chile)

  • Marc G. Genton

    (King Abdullah University of Science and Technology)

Abstract

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.

Suggested Citation

  • Sagnik Mondal & Reinaldo B. Arellano-Valle & Marc G. Genton, 2024. "A multivariate modified skew-normal distribution," Statistical Papers, Springer, vol. 65(2), pages 511-555, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01397-1
    DOI: 10.1007/s00362-023-01397-1
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    References listed on IDEAS

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    3. Christophe Ley & Davy Paindaveine, 2010. "On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 235-250.
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