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Flexible Log-Linear Birnbaum–Saunders Model

Author

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  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Córdoba 230027, Colombia
    Programa de Pós-Graduação em Modelagem e Métodos Quantitativos, Universidade Federal do Ceará, Fortaleza 60020-181, Brazil)

  • Inmaculada Barranco-Chamorro

    (Departamento de Estadística e I.O., Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain)

  • Héctor W. Gómez

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

Rieck and Nedelman (1991) introduced the sinh-normal distribution. This model was built as a transformation of a N(0,1) distribution. In this paper, a generalization based on a flexible skew normal distribution is introduced. In this way, a more general model is obtained that can describe a range of asymmetric, unimodal and bimodal situations. The paper is divided into two parts. First, the properties of this new model, called flexible sinh-normal distribution, are obtained. In the second part, the flexible sinh-normal distribution is related to flexible Birnbaum–Saunders, introduced by Martínez-Flórez et al. (2019), to propose a log-linear model for lifetime data. Applications to real datasets are included to illustrate our findings.

Suggested Citation

  • Guillermo Martínez-Flórez & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2021. "Flexible Log-Linear Birnbaum–Saunders Model," Mathematics, MDPI, vol. 9(11), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1188-:d:561288
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6069 is not listed on IDEAS
    2. 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.
    3. Heleno Bolfarine & Guillermo Martínez-Flórez & Hugo S. Salinas, 2018. "Bimodal symmetric-asymmetric power-normal families," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(2), pages 259-276, January.
    4. Jimmy Reyes & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2020. "Generalized modified slash distribution with applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 2025-2048, April.
    5. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    6. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    7. Chan, P.S. & Ng, H.K.T. & Balakrishnan, N. & Zhou, Q., 2008. "Point and interval estimation for extreme-value regression model under Type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4040-4058, April.
    8. 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.
    9. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    10. 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.
    11. 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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