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The Extended Half-Skew Normal Distribution

Author

Listed:
  • Karol I. Santoro

    (Department of Mathematics, Faculty of Sciences, North Catholic University, Antofagasta 1240000, Chile)

  • Héctor J. Gómez

    (Department of Physics and Mathematics Sciences, Faculty of Engineering, Catholic University of Temuco, Temuco 4780000, Chile)

  • Diego I. Gallardo

    (Department of Mathematics, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile)

  • Inmaculada Barranco-Chamorro

    (Department of Statistics and Operations Research, Faculty of Mathematics, University of Seville, 41012 Seville, Spain)

  • Héctor W. Gómez

    (Department of Mathematics, Faculty of Basic Sciences, University of Antofagasta, Antofagasta 1240000, Chile)

Abstract

A new class of densities for modelling non-negative data, which is based on the skew-symmetric family of distributions proposed by Azzalini is introduced.We focus on the model generated by the skew-normal distribution, called Extended Half Skew-Normal distribution. Its relevant properties are studied. These are pdf, cdf, moments, mgf, and stochastic representation. The parameters are estimated by moment and maximum likelihood methods. A simulation study to assess the performance of the maximum likelihood estimators in finite samples was carried out. Two real applications are included, in which the EHSN provides a better fit than other proposals in the literature.

Suggested Citation

  • Karol I. Santoro & Héctor J. Gómez & Diego I. Gallardo & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2022. "The Extended Half-Skew Normal Distribution," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3740-:d:939429
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    References listed on IDEAS

    as
    1. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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