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

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 t...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-06, Vol.12 (11), p.1762
Main Authors: Gómez, Héctor J, Santoro, Karol I, Ayma, Diego, Cortés, Isaac E, Gallardo, Diego I, Magalhães, Tiago M
Format: Article
Language:English
Subjects:
Adultery
Body size
Carotene
Distribution (Probability theory)
Gumbel distribution
Mathematical research
Maximum likelihood estimators
Quantile regression
Quantiles
Random variables
Regression models
truncated distribution
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12111762