Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model

Roger Tovar-Falón, Guillermo Martínez-Flórez and Heleno Bolfarine
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Roger Tovar-Falón: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
Guillermo Martínez-Flórez: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
Heleno Bolfarine: Departamento de Estatística, Universidade de São Paulo, Sao Paulo 05508-090, Brazil

Mathematics, 2022, vol. 10, issue 7, 1-16

Abstract: In this paper, we propose a linear regression model in which the error term follows a log-gamma-normal (LGN) distribution. The assumption of LGN distribution gives flexibility to accommodate skew forms to the left and to the right. Kurtosis greater or smaller than the normal model can also be accommodated. The regression model for censored asymmetric data is also considered (censored LGN model). Parameter estimation is implemented using the maximum likelihood approach and a small simulation study is conducted to evaluate parameter recovery. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. Results for two applications of the proposed model to real datasets are provided for illustrative purposes.

Keywords: log-gamma-normal distribution; linear regression models; asymmetric data; censored data; maximum likelihood estimators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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