Extended Generalized Sinh-Normal Distribution

Guillermo Martínez-Flórez, David Elal-Olivero and Carlos Barrera-Causil
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Guillermo Martínez-Flórez: Departamento de Matemática y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230001, Colombia
David Elal-Olivero: Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
Carlos Barrera-Causil: Grupo de Investigación Davinci, Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano, Medellín 050034, Colombia

Mathematics, 2021, vol. 9, issue 21, 1-24

Abstract: Positively skewed data sets are common in different areas, and data sets such as material fatigue, reaction time, neuronal reaction time, agricultural engineering, and spatial data, among others, need to be fitted according to their features and maintain a good quality of fit. Skewness and bimodality are two of the features that data sets like this could present simultaneously. So, flexible statistical models should be proposed in this sense. In this paper, a general extended class of the sinh-normal distribution is presented. Additionally, the asymmetric distribution family is extended, and as a natural extension of this model, the extended Birnbaum–Saunders distribution is studied as well. The proposed model presents a better goodness of fit compared to the other studied models.

Keywords: bimodality; Birnbaum–Saunders; maximum likelihood estimation; moments; positively skewed model; sinh-normal distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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