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The bivariate Sinh-Elliptical distribution with applications to Birnbaum–Saunders distribution and associated regression and measurement error models

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  • Vilca, Filidor
  • Balakrishnan, N.
  • Zeller, Camila Borelli

Abstract

The bivariate Sinh-Elliptical (BSE) distribution is a generalization of the well-known Rieck’s (1989) Sinh-Normal distribution that is quite useful in Birnbaum–Saunders (BS) regression model. The main aim of this paper is to define the BSE distribution and discuss some of its properties, such as marginal and conditional distributions and moments. In addition, the asymptotic properties of method of moments estimators are studied, extending some existing theoretical results in the literature. These results are obtained by using some known properties of the bivariate elliptical distribution. This development can be viewed as a follow-up to the recent work on bivariate Birnbaum–Saunders distribution by Kundu et al. (2010) towards some applications in the regression setup. The measurement error models are also introduced as part of the application of the results developed here. Finally, numerical examples using both simulated and real data are analyzed, illustrating the usefulness of the proposed methodology.

Suggested Citation

  • Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "The bivariate Sinh-Elliptical distribution with applications to Birnbaum–Saunders distribution and associated regression and measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 1-16.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:1-16
    DOI: 10.1016/j.csda.2014.06.001
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    References listed on IDEAS

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    1. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
    2. 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.
    3. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.
    4. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    5. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
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    Cited by:

    1. Vilca, Filidor & Romeiro, Renata G. & Balakrishnan, N., 2016. "A bivariate Birnbaum–Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 169-183.
    2. Filidor Vilca & Camila Borelli Zeller & Gauss M. Cordeiro, 2015. "The sinh-normal/independent nonlinear regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1659-1676, August.
    3. Debasis Kundu, 2017. "On Multivariate Log Birnbaum-Saunders Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 292-315, November.
    4. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.

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