**5. Conclusions**

We have introduced a new family of distributions able to model skewness, unimodality and bimodality in the BS distribution. We have discussed several of its properties. Explicit expressions for the cdf are given in terms of the cdf of a bivariate normal variable. Non-linear equations to obtain the modes of this distribution are provided. The estimation of parameters is carried out via maximum likelihood. We highlight that the ML equations must be solved by using iterative methods. The information matrix is non-singular and therefore likelihood ratio tests to compare this model with other nested models can be implemented. The interest and flexibility of our proposal is supported with two illustrations to real data in which we show that:


Therefore the outcome of these practical demonstrations show that the new family is very flexible and widely applicable.

*Symmetry* **2019**, *11*, 1305

**Author Contributions:** All the authors contributed significantly to the present paper.

**Funding:** The research of G. Martínez-Flórez was supported by Grant Proyecto Universidad de Córdoba: Distribuciones de probabilidad asimétrica bimodal con soporte positivo (Colombia). The research of I. Barranco-Chamorro was supported by Grant CTM2015-68276-R (Spain). H.W. Gómez was supported by Grant SEMILLERO UA-2019 (Chile).

**Acknowledgments:** The authors would like to thank the editor and the anonymous referees for their comments and suggestions, which significantly improved our manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
