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Extended Generalized Sinh-Normal Distribution

Author

Listed:
  • Guillermo Martínez-Flórez

    (Departamento de Matemática y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230001, Colombia
    Present address: Programa de Pós-Graduação em Modelagem e Métodos Quantitativos, Universidade Federal do Ceará, Fortaleza 60020-181, Brazil.)

  • David Elal-Olivero

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

  • Carlos Barrera-Causil

    (Grupo de Investigación Davinci, Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano, Medellín 050034, Colombia)

Abstract

Positively skewed data sets are common in different areas, and data sets such as material fatigue, reaction time, neuronal reaction time, agricultural engineering, and spatial data, among others, need to be fitted according to their features and maintain a good quality of fit. Skewness and bimodality are two of the features that data sets like this could present simultaneously. So, flexible statistical models should be proposed in this sense. In this paper, a general extended class of the sinh-normal distribution is presented. Additionally, the asymmetric distribution family is extended, and as a natural extension of this model, the extended Birnbaum–Saunders distribution is studied as well. The proposed model presents a better goodness of fit compared to the other studied models.

Suggested Citation

  • Guillermo Martínez-Flórez & David Elal-Olivero & Carlos Barrera-Causil, 2021. "Extended Generalized Sinh-Normal Distribution," Mathematics, MDPI, vol. 9(21), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2793-:d:671843
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    References listed on IDEAS

    as
    1. Neveka M. Olmos & Guillermo Martínez-Flórez & Heleno Bolfarine, 2017. "Bimodal Birnbaum–Saunders distribution with applications to non negative measurements," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6240-6257, July.
    2. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    3. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    4. Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    5. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    6. 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.
    7. P. M. Hartigan, 1985. "Computation of the Dip Statistic to Test for Unimodality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 320-325, November.
    8. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    9. Nabor Castillo & Héctor Gómez & Heleno Bolfarine, 2011. "Epsilon Birnbaum–Saunders distribution family: properties and inference," Statistical Papers, Springer, vol. 52(4), pages 871-883, November.
    10. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor W. Gómez, 2017. "The Log-Linear Birnbaum-Saunders Power Model," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 913-933, September.
    11. Milton A. Cortés & David Elal-Olivero & Juan F. Olivares-Pacheco, 2018. "A New Class of Distributions Generated by the Extended Bimodal-Normal Distribution," Journal of Probability and Statistics, Hindawi, vol. 2018, pages 1-10, November.
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