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On Properties of the Bimodal Skew-Normal Distribution and an Application

Author

Listed:
  • David Elal-Olivero

    (Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Juan F. Olivares-Pacheco

    (Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Osvaldo Venegas

    (Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile)

  • Heleno Bolfarine

    (Instituto de Matemática e Estatística (IME), Universidade de São Paulo, São Paulo 05508-090, Brazil)

  • Héctor W. Gómez

    (Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

Suggested Citation

  • David Elal-Olivero & Juan F. Olivares-Pacheco & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2020. "On Properties of the Bimodal Skew-Normal Distribution and an Application," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:703-:d:353320
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    References listed on IDEAS

    as
    1. Yanyuan Ma & Marc G. Genton, 2004. "Flexible Class of Skew‐Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 459-468, September.
    2. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    3. 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.
    4. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
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