An Asymmetric Bimodal Distribution with Application to Quantile Regression

An Asymmetric Bimodal Distribution with Application to Quantile Regression

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 likeli...

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Main Authors: Yolanda M. Gómez, Emilio Gómez-Déniz, Osvaldo Venegas, Diego I. Gallardo, Héctor W. Gómez
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Symmetry
Subjects:
asymmetric bimodal distribution
bimodal
maximum likelihood
Online Access:https://www.mdpi.com/2073-8994/11/7/899
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spelling doaj-c510b8d6035d42f69411afb411b59c452020-11-24T21:37:59ZengMDPI AGSymmetry2073-89942019-07-0111789910.3390/sym11070899sym11070899An Asymmetric Bimodal Distribution with Application to Quantile RegressionYolanda M. Gómez0Emilio Gómez-Déniz1Osvaldo Venegas2Diego I. Gallardo3Héctor W. Gómez4Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, ChileDepartment of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, SpainDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChileDepartamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, ChileDepartamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileIn 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.https://www.mdpi.com/2073-8994/11/7/899asymmetric bimodal distributionbimodalmaximum likelihood
collection DOAJ
language English
format Article
sources DOAJ
author Yolanda M. Gómez
Emilio Gómez-Déniz
Osvaldo Venegas
Diego I. Gallardo
Héctor W. Gómez
spellingShingle Yolanda M. Gómez
Emilio Gómez-Déniz
Osvaldo Venegas
Diego I. Gallardo
Héctor W. Gómez
An Asymmetric Bimodal Distribution with Application to Quantile Regression
Symmetry
asymmetric bimodal distribution
bimodal
maximum likelihood
author_facet Yolanda M. Gómez
Emilio Gómez-Déniz
Osvaldo Venegas
Diego I. Gallardo
Héctor W. Gómez
author_sort Yolanda M. Gómez
title An Asymmetric Bimodal Distribution with Application to Quantile Regression
title_short An Asymmetric Bimodal Distribution with Application to Quantile Regression
title_full An Asymmetric Bimodal Distribution with Application to Quantile Regression
title_fullStr An Asymmetric Bimodal Distribution with Application to Quantile Regression
title_full_unstemmed An Asymmetric Bimodal Distribution with Application to Quantile Regression
title_sort asymmetric bimodal distribution with application to quantile regression
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-07-01
description 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.
topic asymmetric bimodal distribution
bimodal
maximum likelihood
url https://www.mdpi.com/2073-8994/11/7/899
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