[Invited tutorial] Birnbaum–Saunders regression models: a comparative evaluation of three approaches

Alan Dasilva, Renata Dias, Victor Leiva, Carolina Marchant, Helton Saulo

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12 Scopus citations


This study investigates three regression models based on the Birnbaum–Saunders distribution. The first model is obtained directly through the Birnbaum–Saunders distribution; the second model is obtained via a logarithmic transformation in the response variable; and the third model employs a mean parametrization of this distribution. The primary objective of this study is to compare the performance of the three Birnbaum–Saunders regression models. The secondary objective is to provide a tool to choose the best model for regression when analysing data following a Birnbaum–Saunders distribution. By using Monte Carlo simulations and the R software, we evaluate the behaviour of the corresponding estimators, and of the Cox–Snell and randomized quantile residuals. An illustration with real data is provided to compare the investigated regression models.

Original languageEnglish
Pages (from-to)2552-2570
Number of pages19
JournalJournal of Statistical Computation and Simulation
Issue number14
StatePublished - 21 Sep 2020


  • Birnbaum–Saunders distributions
  • Monte Carlo method
  • R software
  • maximum likelihood estimators
  • residuals


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