The sinh-normal/independent nonlinear regression model

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.

Keywords:

• nonlinear regression
• Birnbaum–Saunders distribution
• EM-algorithm
• Robust estimation
• normal/independent distribution
• sinh-normal distribution

Acknowledgements

The authors wish to thank the Editor-in-Chief, and two anonymous referees for their constructive comments on an earlier version of this manuscript, which resulted in this improved version. This work was supported by CNPq-Brazil (309086/2009-4) and FAPEMIG-Brazil (APQ-01520-12).

Disclosure statement

No potential conflict of interest was reported by the author(s).