Simple robust parameter estimation for the Birnbaum-Saunders distribution

Abstract

We study the problem of robust estimation for the two-parameter Birnbaum-Saunders distribution. It is well known that the maximum likelihood estimator (MLE) is efficient when the underlying model is true but at the same time it is quite sensitive to data contamination that is often encountered in practice. In this paper, we propose several estimators which have simple closed forms and are also robust to data contamination. We study the breakdown points and asymptotic properties of the proposed estimators. These estimators are then applied to both simulated and real datasets. Numerical results show that the proposed estimators are attractive alternative to the MLE in that they are quite robust to data contamination and also highly efficient when the underlying model is true.

Discussion of Birnbaum‐Saunders distribution: A review of models, analysis, and applications

“…Few articles have been published on the analysis of censored data in the BS distribution based on heavy‐tailed distributions, even in the associated regression model. Some results can be found in the works of Barros et al and Lachos et al (3)From the close relationship of the BS distribution with the normal distribution as in , one may point out the lack of robustness in the parameter estimation with departure from normality or in the presence of outliers . This aspect is the starting point to study techniques based on the robust estimators or heavy‐tailed distributions.…”

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

“…For different inference‐related issues, one may refer to the works of Ahmed et al, Arellano‐Valle et al, Athayde et al, Audrey et al, Azevedo et al, Balakrishnan et al, Balakrishnan and Zhu, Barros et al, Chang and Tang, Cordeiro et al, Cysneiros et al, Desmond and Yang, Farias and Lemonte, Guo et al, Jeng, Lachos et al, Lemonte, Lemonte and Cordeiro, Lemonte et al, Lemonte and Ferrari, Lemonte and Patriota, Li et al, Li and Xu, Lillo et al, Lu and Chang, Meintanis, Moala et al, Niu et al, Padgett and Tomlinson, Pérez and Correa, Qu and Xie, Riquelme et al, Sánchez et al, Santana et al, Santos‐Neto et al, Saulo et al, Sha and Ng, Teimouri et al, Tsionas, Upadhyay and Mukherjee, Vanegas and Paula, Vanegas et al, Vilca et al, Wang, Wang and Fei, Wang et al, Xiao et al, Xie and Wei, Xu and Tang, Xu et al, Zhu and Balakrishnan, and the references cited therein.…”

Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

“…Leiva et al suggested capability indices for BS processes applied to electronic and food industries. Wang et al contributed, proposing simple robust parameter estimators.…”