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A Bimodal Extension of the Epsilon-Skew-Normal Model

Author

Listed:
  • Juan Duarte

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

  • Guillermo Martínez-Flórez

    (Departamento de Matemática y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia)

  • Diego Ignacio Gallardo

    (Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 7820436, Chile)

  • Osvaldo Venegas

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

  • Héctor W. Gómez

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

Abstract

This article introduces a bimodal model based on the epsilon-skew-normal distribution. This extension generates bimodal distributions similar to those produced by the mixture of normal distributions. We study the basic properties of this new family. We apply maximum likelihood estimators, calculate the information matrix and present a simulation study to assess parameter recovery. Finally, we illustrate the results to three real data sets, suggesting this new distribution as a plausible alternative for modelling bimodal data.

Suggested Citation

  • Juan Duarte & Guillermo Martínez-Flórez & Diego Ignacio Gallardo & Osvaldo Venegas & Héctor W. Gómez, 2023. "A Bimodal Extension of the Epsilon-Skew-Normal Model," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:507-:d:1039384
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6069 is not listed on IDEAS
    2. 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.
    3. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 1-13, April.
    4. Altemir da Silva Braga & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "A new skew-bimodal distribution with applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(12), pages 2950-2968, June.
    5. 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.
    6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    7. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
    8. M.Y. Hassan & M.Y. El-Bassiouni, 2016. "Bimodal skew-symmetric normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1527-1541, March.
    9. S. Shafiei & M. Doostparast, 2014. "Balakrishnan Skew-t Distribution and Associated Statistical Characteristics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(19), pages 4109-4122, October.
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