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The information matrix of the bivariate extended skew-normal distribution

Author

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  • Stefano Franco

    (Independent Consultant in Statistics, ML, and AI)

  • Adelchi Azzalini

    (Università degli Studi di Padova)

Abstract

For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the bivariate case. Specifically, we derive explicit expressions for the score function and the information matrix, in the observed and the expected form; these do not appear to have been examined before in the literature. Ensuing numerical work illustrates some relevant aspects of the expected information matrix.

Suggested Citation

  • Stefano Franco & Adelchi Azzalini, 2025. "The information matrix of the bivariate extended skew-normal distribution," METRON, Springer;Sapienza Università di Roma, vol. 83(2), pages 235-259, August.
    • Handle: RePEc:spr:metron:v:83:y:2025:i:2:d:10.1007_s40300-024-00278-3
    DOI: 10.1007/s40300-024-00278-3
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    References listed on IDEAS

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    1. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    2. Christopher J. Adcock, 2022. "Properties and Limiting Forms of the Multivariate Extended Skew-Normal and Skew-Student Distributions," Stats, MDPI, vol. 5(1), pages 1-42, March.
    3. Monica Chiogna, 2005. "A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 331-341, December.
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