*Article* **An Asymmetric Bimodal Distribution with Application to Quantile Regression**

### **Yolanda M. Gómez 1, Emilio Gómez-Déniz 2, Osvaldo Venegas 3,\*, Diego I. Gallardo 1 and Héctor W. Gómez 4**


Received: 27 May 2019; Accepted: 25 June 2019; Published: 10 July 2019

**Abstract:** In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data.

**Keywords:** asymmetric bimodal distribution; bimodal; maximum likelihood
