**4. Numerical Illustrations**

The numerical illustrations introduced next are aimed to show that the FBS model can be an alternative to modelling unimodal or bimodal data from different areas. First illustration is related to nickel content in soil samples analyzed at the Mining Department (Departamento de Minas) of Universidad de Atacama, Chile. We start by showing that both, BS and skew-BS (SBS) models are not able to capture bimodality present in this data set. Thus, the FBS model turned out to be a good option, to fit the data even better than a mixture of two normal distributions, which is another competing alternative to fit bimodal data. Second illustration is related to air pollution in New York city in USA, which was previously analyzed in [16,30]. In this case, it is shown that FBS model again provides a better fit than BS and SBS. As competing model the extended Birnbaum-Saunders (EBS) is also considered. Recall that the *EBS*(*<sup>α</sup>*, *β*, *σ*, *ν*, *λ*) is a five-parameter model proposed in [16] where the parameter *σ* affects the kurtosis; *ν* and *λ* affect the skewness; and *α* and *β* the shape and scale as in the usual BS model. We highlight that, for this dataset, the *FBS*(*<sup>α</sup>*, *β*, *δ*, *λ*) model provides a better fit than that given by the *EBS*(*<sup>α</sup>*, *β*, *σ*, *ν*, *λ*) in [16] with the merit of using less parameters.
