New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses

Guillermo Martínez-Flórez, Rafael B. Azevedo-Farias and Roger Tovar-Falón ()
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Guillermo Martínez-Flórez: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
Rafael B. Azevedo-Farias: Department of Statistics and Applied Mathematics, Federal University of Ceara, Fortaleza 60455-670, Brazil
Roger Tovar-Falón: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia

Mathematics, 2022, vol. 10, issue 17, 1-24

Abstract: Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response variable based on a set of covariates. Despite the great usefulness of this distribution to fit the responses on the ( 0 , 1 ) unit interval, its relevance loses objectivity when the interest is quantifying the influence of these covariates on the quantiles of the variable response in ( 0 , 1 ) ; being the most critical situation when the distribution presents high asymmetry and/or kurtosis. The main objective of this work is to introduce a distribution for modeling rates and proportions. The introduced distribution is obtained from the alpha-power extension of the skew–normal distribution, which is known in the literature as the power–skew–normal distribution.

Keywords: unit distribution; linear regression; maximum likelihood estimation; score function; information matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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