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The sinh-normal/independent nonlinear regression model

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  • Filidor Vilca
  • Camila Borelli Zeller
  • Gauss M. Cordeiro

Abstract

The normal/independent family of distributions is an attractive class of symmetric heavy-tailed density functions. They have a nice hierarchical representation to make inferences easily. We propose the Sinh-normal/independent distribution which extends the Sinh-normal (SN) distribution [23]. We discuss some of its properties and propose the Sinh-normal/independent nonlinear regression model based on a similar setup of Lemonte and Cordeiro [18], who applied the Birnbaum-Saunders distribution. We develop an EM-algorithm for maximum likelihood estimation of the model parameters. In order to examine the robustness of this flexible class against outlying observations, we perform a simulation study and analyze a real data set to illustrate the usefulness of the new model.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:8:p:1659-1676
    DOI: 10.1080/02664763.2015.1005059
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    References listed on IDEAS

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    1. 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.
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    3. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
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    5. Galea, Manuel & Paula, Gilberto A. & Cysneiros, Francisco José A., 2005. "On diagnostics in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 459-467, July.
    6. Leiva, Victor & Riquelme, Marco & Balakrishnan, N. & Sanhueza, Antonio, 2008. "Lifetime analysis based on the generalized Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2079-2097, January.
    7. 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.
    8. Lemonte, Artur J. & Cordeiro, Gauss M., 2009. "Birnbaum-Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4441-4452, October.
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    1. Filidor Vilca & Caio L. N. Azevedo & N. Balakrishnan, 2017. "Bayesian inference for sinh-normal/independent nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2052-2074, August.
    2. Rocío Maehara & Heleno Bolfarine & Filidor Vilca & N. Balakrishnan, 2021. "A robust Birnbaum–Saunders regression model based on asymmetric heavy-tailed distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1049-1080, October.

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