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New Regression Models Based on the Unit-Sinh-Normal Distribution: Properties, Inference, and Applications

Author

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  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230027, Colombia
    These authors contributed equally to this work.)

  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230027, Colombia
    These authors contributed equally to this work.)

Abstract

In this paper, two new distributions were introduced to model unimodal and/or bimodal data. The first distribution, which was obtained by applying a simple transformation to a unit-Birnbaum–Saunders random variable, is useful for modeling data with positive support, while the second is appropriate for fitting data on the (0,1) interval. Extensions to regression models were also studied in this work, and statistical inference was performed from a classical perspective by using the maximum likelihood method. A small simulation study is presented to evaluate the benefits of the maximum likelihood estimates of the parameters. Finally, two applications to real data sets are reported to illustrate the developed methodology.

Suggested Citation

  • Guillermo Martínez-Flórez & Roger Tovar-Falón, 2021. "New Regression Models Based on the Unit-Sinh-Normal Distribution: Properties, Inference, and Applications," Mathematics, MDPI, vol. 9(11), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1231-:d:564018
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    References listed on IDEAS

    as
    1. N. Balakrishnan & Xiaojun Zhu, 2015. "Inference for the bivariate Birnbaum–Saunders lifetime regression model and associated inference," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 853-872, October.
    2. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
    3. Andréa Rocha & Alexandre Simas, 2011. "Influence diagnostics in a general class of beta regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 95-119, May.
    4. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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