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An Exponentiated Multivariate Extension for the Birnbaum-Saunders Log-Linear Model

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  • Guillermo Martínez-Flórez

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

  • Rafael Bráz Azevedo-Farias

    (Department of Statistics and Applied Mathematics, Federal University of Ceara, Fortaleza 60455-670, Brazil
    These authors contributed equally to this work.)

  • Roger Tovar-Falón

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

Abstract

In this work, a bivariate extension of the univariate exponentiated sinh-normal distribution is proposed. The properties of the new distribution, which is called the bivariate exponentiated sinh-normal distribution, are studied in detail, and the maximum likelihood method is considered to estimate the unknown model parameters. In addition, the extension of the new distribution to the case of regression models is proposed. Monte Carlo simulation experiments are carried out to investigate the performance of the used estimation method, and two applications to real datasets are presented for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1299-:d:793606
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    References listed on IDEAS

    as
    1. Ramesh Gupta & Rameshwar Gupta, 2004. "Generalized skew normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 501-524, December.
    2. 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.
    3. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    4. 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.
    5. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
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    Cited by:

    1. 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.
    2. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    3. 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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