*Article* **Flexible Birnbaum–Saunders Distribution**

### **Guillermo Martínez-Flórez 1, Inmaculada Barranco-Chamorro 2, Heleno Bolfarine 3 and Héctor W. Gómez 4,\***


Received: 5 September 2019; Accepted: 4 October 2019; Published: 16 October 2019

**Abstract:** In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models.

**Keywords:** flexible skew-normal distribution; skew Birnbaum–Saunders distribution; bimodality; maximum likelihood estimation; Fisher information matrix
