A Unification of Families of Birnbaum–Saunders Distributions with Applications

Abstract

This paper considers an extension for the skew-elliptical Birnbaum–Saunders model by considering the power-normal model. Some properties of this family are studied and it is shown, in particular, that the range of asymmetry and kurtosis surpasses that of the ordinary skew-normal and power[1]normal models. Estimation is dealt with by using the maximum likelihood approach. Observed and expected information matrices are derived and it is shown to be nonsingular at the vicinity of symmetry. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models.

Keywords

• elliptical Birnbaum–Saunders distribution
• maximum likelihood
• power-normal distribution