[Invited tutorial] Birnbaum-Saunders regression models: a comparative evaluation of three approaches. (English) Zbl 07480192
Summary: 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.
MSC:
| 62-XX | Statistics |
Keywords:
Birnbaum-Saunders distributions; maximum likelihood estimators; Monte Carlo method; residualsReferences:
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