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The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model

Author

Listed:
  • 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.)

  • Artur J. Lemonte

    (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078970, RN, Brazil
    These authors contributed equally to this work.)

  • Germán Moreno-Arenas

    (Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga 680006, Colombia)

  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia)

Abstract

In this paper, a new bivariate absolutely continuous probability distribution is introduced. The new distribution, which is called the bivariate unit-sinh-normal (BVUSHN) distribution, arises by applying a transformation to the bivariate Birnbaum–Saunders distribution (BVBS). The main properties of the new proposal are studied in detail. In addition, from the new distribution, the BVUSHN regression model is also introduced. For both the bivariate probability distribution and the respective associated regression model, parameter estimation is conducted from a classical approach by using the maximum likelihood method together with the two-step estimation method. A small Monte Carlo simulation study is carried out to evaluate the behavior of the used estimation method and the properties of the estimators. Finally, for illustrative purposes, two applications with real data are presented in which the usefulness of the proposals is evidenced.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3125-:d:902925
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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.
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    5. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, A., 2010. "Bivariate Birnbaum-Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 113-125, January.
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