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

Rocío Maehara, Heleno Bolfarine, Filidor Vilca () and N. Balakrishnan
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Rocío Maehara: Universidad del Pacífico
Heleno Bolfarine: Universidade Estadual de São Paulo
Filidor Vilca: Universidade Estadual de Campinas
N. Balakrishnan: McMaster University

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 7, No 5, 1049-1080

Abstract: Abstract 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.

Keywords: Nonlinear regression models; Birnbaum–Saunders distribution; EM algorithm; Robust estimation; Skew-normal/independent distribution; Sinh-normal distribution (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-021-00815-4

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