A log-Birnbaum–Saunders regression model with asymmetric errors

Abstract

This paper introduces a skewed log-Birnbaum–Saunders regression model based on the skewed sinh-normal distribution proposed by Leiva et al. [A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426–443]. Some influence methods, such as the local influence and generalized leverage, are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.

Keywords:

• Birnbaum–Saunders distribution
• fatigue life distribution
• influence diagnostic
• sinh-normal distribution
• skew-normal distribution

Acknowledgements

The author thanks an anonymous referee for helpful comments. The financial support from FAPESP (Brazil) is gratefully acknowledged.