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An Asymmetric Bimodal Distribution with Application to Quantile Regression

Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
Department of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 899;
Received: 27 May 2019 / Revised: 25 June 2019 / Accepted: 25 June 2019 / Published: 10 July 2019
PDF [2964 KB, uploaded 10 July 2019]


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. View Full-Text
Keywords: asymmetric bimodal distribution; bimodal; maximum likelihood asymmetric bimodal distribution; bimodal; maximum likelihood

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Gómez, Y.M.; Gómez-Déniz, E.; Venegas, O.; Gallardo, D.I.; Gómez, H.W. An Asymmetric Bimodal Distribution with Application to Quantile Regression. Symmetry 2019, 11, 899.

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