A robust Birnbaum–Saunders regression model based on asymmetric heavy-tailed distributions

Rocío Maehara, Heleno Bolfarine, Filidor Vilca, N. Balakrishnan

Research output: Contribution to journalArticle in a journalpeer-review

2 Scopus citations


Skew-normal/independent distributions provide an attractive class of asymmetric heavy-tailed distributions to the usual symmetric normal distribution. We use this class of distributions here to derive a robust generalization of sinh-normal distributions (Rieck in Statistical analysis for the Birnbaum–Saunders fatigue life distribution, 1989), we then propose robust nonlinear regression models, generalizing the Birnbaum–Saunders regression models proposed by Rieck and Nedelman (Technometrics 33:51–60, 1991) that have been studied extensively. The proposed regression models have a nice hierarchical representation that facilitates easy implementation of an EM algorithm for the maximum likelihood estimation of model parameters and provide a robust alternative to estimation of parameters. Simulation studies as well as applications to a real dataset are presented to illustrate the usefulness of the proposed model as well as all the inferential methods developed here.

Original languageEnglish
Pages (from-to)1049-1080
Number of pages32
Issue number7
Early online date13 Apr 2021
StatePublished - Oct 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Birnbaum–Saunders distribution
  • EM algorithm
  • Nonlinear regression models
  • Robust estimation
  • Sinh-normal distribution
  • Skew-normal/independent distribution


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