Bimodal Regression Model

Modelo de regresión Bimodal

Regression analysis is a technique widely used in different areas ofhuman knowledge, with distinct distributions for the error term. Itis the case, however, that regression models with bimodal responsesor, equivalently, with the error term following a bimodal distribution are notcommon in the literature, perhaps due to the lack of simple to dealwith bimodal error distributions. In this paper we propose a simpleto deal with bimodal regression model with a symmetric-asymmetricdistribution for the error term for which for some values of theshape parameter it can be bimodal. This new distribution containsthe normal and skew-normal as special cases. A realdata application reveals that the new model can be extremely usefulin such situations.

El análisis de regresión es una técnica muy utilizada en diferentes áreas de conocimiento humano, con diferentes distribuciones para el término de error, sin embargo los modelos de regresión con el termino de error siguiendo una distribución bimodal no son comunes en la literatura, tal vez por la simple razón de no tratar con errores con distribución bimodal. En este trabajo proponemos un camino sencillo para hacer frente a modelos de regresión bimodal con una distribución simétrica - asimétrica para el término de error para la cual para algunos valores del parámetro de forma esta puede ser bimodal. Esta nueva distribución contiene a la distribución normal y la distribución normal asimétrica como casos especiales. Una aplicación con datos reales muestra que el nuevo modelo puede ser extremadamente útil en algunas situaciones.

https://doi.org/10.15446/rce.v40n1.51738

Bimodal Regression Model Modelo de regresión Bimodal GUILLERMO MARTÍNEZ-FLÓREZ¹, HUGO S. SALINAS², HELENO BOLFARINE³

¹Universidad de Córdoba, Facultad de Ciencias Básicas, Departamento de Matemáticas y Estadística, Córdoba, Colombia. PhD. Email: gmartinez@correo.unicordoba.edu.co
²Universidad de Atacama, Facultad de Ingenieróia, Departamento de Matemóatica, Copiapó, Chile. PhD. Email: hugo.salinas@uda.cl
³Universidad de Sao Paulo, IME, Departamento de Estatóistica, Sao Paulo, Brasil. PhD. Email: hbolfar@ime.usp.br

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Abstract

Regression analysis is a technique widely used in different areas of human knowledge, with distinct distributions for the error term. It is the case, however, that regression models with the error term following a bimodal distribution are not common in the literature, perhaps due to the lack of simple to deal with bimodal error distributions. In this paper, we propose a simple to deal with bimodal regression model with a symmetric-asymmetric distribution for the error term for which for some values of the shape parameter it can be bimodal. This new distribution contains the normal and skew-normal as special cases. A real data application reveals that the new model can be extremely useful in such situations.

Key words: Bimodal Distribution, Generalized Gaussian Distribution, Linear Regression, Power Regression Model.

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Resumen

Palabras clave: distribución bimodal, distribución gaussiana generalizada, regresión lineal, modelo de regresión exponenciado.

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Texto completo disponible en PDF

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[Recibido en abril de 2015. Aceptado en febrero de 2016]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv40n1a03,
    AUTHOR  = {Martínez-Flórez, Guillermo and Salinas, Hugo S. and Bolfarine, Heleno},
    TITLE   = {{Bimodal Regression Model}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2017},
    volume  = {40},
    number  = {1},
    pages   = {65-83}
}

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