Statistical Modelling 14 (1) (2014), 21–48

Birnbaum–Saunders statistical modelling: a new approach

Víctor Leiva Departamento de Estadística,
Universidad de Valparaíso,
Chile
e-mail: victor.leiva@uv.cl

Manoel Santos-Neto
Departamento de Estatística,
Universidade Federal de Campina Grande,
Brazil


Francisco José A Cysneiros
Departamento de Estatística,
Universidade Federal de Pernambuco,
Brazil


Michelli Barros
Departamento de Estatística,
Universidade Federal de Campina Grande,
Brazil


Abstract:

Modelling based on the Birnbaum–Saunders distribution has received considerable attention in recent years. In this article, we introduce a new approach for Birnbaum–Saunders regression models, which allows us to analyze data in their original scale and to model non-constant variance. In addition, we propose four types of residuals for these models and conduct a simulation study to establish which of them has a better performance. Moreover, we develop methods of local influence by calculating the normal curvatures under different perturbation schemes. Finally, we perform a statistical analysis with real data by using the approach proposed in the article. This analysis shows the potentiality of our proposal.

Keywords:

Birnbaum–Saunders; distribution; data analysis; influence diagnostics; Monte Carlo methods; reparameterization residuals

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