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The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model

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  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Sandra Vergara-Cardozo

    (Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá 111321, Colombia)

  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Luisa Rodriguez-Quevedo

    (Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá 111321, Colombia)

Abstract

In this article, a multivariate extension of the unit-sinh-normal (USHN) distribution is presented. The new distribution, which is obtained from the conditionally specified distributions methodology, is absolutely continuous, and its marginal distributions are univariate USHN. The properties of the multivariate USHN distribution are studied in detail, and statistical inference is carried out from a classical approach using the maximum likelihood method. The new multivariate USHN distribution is suitable for modeling bounded data, especially in the ( 0 , 1 ) p region. In addition, the proposed distribution is extended to the case of the regression model and, for the latter, the Fisher information matrix is derived. The numerical results of a small simulation study and two applications with real data sets allow us to conclude that the proposed distribution, as well as its extension to regression models, are potentially useful to analyze the data of proportions, rates, or indices when modeling them jointly considering different degrees of correlation that may exist in the study variables is of interest.

Suggested Citation

  • Guillermo Martínez-Flórez & Sandra Vergara-Cardozo & Roger Tovar-Falón & Luisa Rodriguez-Quevedo, 2023. "The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1095-:d:1076828
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    References listed on IDEAS

    as
    1. Guillermo Martínez-Flórez & Rafael Bráz Azevedo-Farias & Roger Tovar-Falón, 2022. "An Exponentiated Multivariate Extension for the Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    2. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    3. Edilberto Cepeda-Cuervo & Jorge Alberto Achcar & Liliana Garrido Lopera, 2014. "Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 677-687, March.
    4. Guillermo Martínez-Flórez & Rafael Bráz Azevedo Farias & Germán Moreno-Arenas, 2017. "Multivariate log-Birnbaum–Saunders regression models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10166-10178, October.
    5. Guillermo Martínez-Flórez & Rafael B. Azevedo-Farias & Roger Tovar-Falón, 2022. "New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    6. 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.
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    Cited by:

    1. Roger Tovar-Falón & Guillermo Martínez-Flórez & Luis Páez-Martínez, 2023. "Bivariate Unit-Weibull Distribution: Properties and Inference," Mathematics, MDPI, vol. 11(17), pages 1-19, September.

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