New Regression Models Based on the Unit-Sinh-Normal Distribution: Properties, Inference, and Applications

Guillermo Martínez-Flórez and Roger Tovar-Falón
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Guillermo Martínez-Flórez: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230027, Colombia
Roger Tovar-Falón: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230027, Colombia

Mathematics, 2021, vol. 9, issue 11, 1-19

Abstract: In this paper, two new distributions were introduced to model unimodal and/or bimodal data. The first distribution, which was obtained by applying a simple transformation to a unit-Birnbaum–Saunders random variable, is useful for modeling data with positive support, while the second is appropriate for fitting data on the (0,1) interval. Extensions to regression models were also studied in this work, and statistical inference was performed from a classical perspective by using the maximum likelihood method. A small simulation study is presented to evaluate the benefits of the maximum likelihood estimates of the parameters. Finally, two applications to real data sets are reported to illustrate the developed methodology.

Keywords: unit-Birnbaum–Saunders distribution; log-sinh-normal regression model; unit-sinh-normal regression model; maximum likelihood method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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