A New Generalization of the Truncated Gumbel Distribution with Quantile Regression and Applications

Héctor J. Gómez (), Karol I. Santoro, Diego Ayma, Isaac E. Cortés, Diego I. Gallardo and Tiago M. Magalhães
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Héctor J. Gómez: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Karol I. Santoro: Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Diego Ayma: Departamento de Matemáticas, Facultad de Ciencias, Universidad Católica del Norte, Antofagasta 1240000, Chile
Isaac E. Cortés: Facultad de Ciencias, Universidad Arturo Prat, Avenida Arturo Prat 2120, Iquique 1110939, Chile
Diego I. Gallardo: Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
Tiago M. Magalhães: Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora 36036-900, MG, Brazil

Mathematics, 2024, vol. 12, issue 11, 1-20

Abstract: In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the p-th quantile of the distribution to perform quantile regression in this model. An extensive simulation study demonstrates the good performance of the maximum likelihood estimators in finite samples. Finally, two applications to real datasets related to the level of beta-carotene and body mass index are presented.

Keywords: Gumbel distribution; maximum likelihood estimators; quantile regression; truncated distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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