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Open AccessArticle
Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile
1
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
2
Departamento de Educación, Facultad de Educación, Universidad de Antofagasta, Antofagasta 1240000, Chile
3
Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
4
Departamento de Procesos Industriales, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
5
Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora 36036-900, Brazil
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(23), 3838; https://doi.org/10.3390/math13233838 (registering DOI)
Submission received: 8 October 2025
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Revised: 6 November 2025
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Accepted: 24 November 2025
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Published: 30 November 2025
Abstract
This study revisits a recently proposed member of the truncated positive family of distributions, referred to as the positively truncated Student’s-t distribution. The distribution retains the structure of the classical Student’s-t distribution while explicitly incorporating a kurtosis parameter, yielding a flexible three-parameter formulation that governs location, scale, and tail behavior. A closed-form quantile function is derived, allowing a novel reparameterization based on the pth quantile and thereby facilitating integration into quantile regression models. The analytical tractability of the quantile function also enables efficient random number generation via the inverse transform method, which supports a comprehensive simulation study demonstrating the strong performance of the proposed estimators, particularly for the degrees-of-freedom parameter. The entire methodology is implemented in the tpn package for the R software. Finally, two real-data applications involving PM2.5 measurements—one without covariates and another with covariates—highlight the model’s robustness and its ability to capture heavy-tailed behavior.
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MDPI and ACS Style
Gómez, H.J.; Santoro, K.I.; Gallardo, D.I.; Leal, P.E.; Magalhães, T.M.
Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile. Mathematics 2025, 13, 3838.
https://doi.org/10.3390/math13233838
AMA Style
Gómez HJ, Santoro KI, Gallardo DI, Leal PE, Magalhães TM.
Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile. Mathematics. 2025; 13(23):3838.
https://doi.org/10.3390/math13233838
Chicago/Turabian Style
Gómez, Héctor J., Karol I. Santoro, Diego I. Gallardo, Paola E. Leal, and Tiago M. Magalhães.
2025. "Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile" Mathematics 13, no. 23: 3838.
https://doi.org/10.3390/math13233838
APA Style
Gómez, H. J., Santoro, K. I., Gallardo, D. I., Leal, P. E., & Magalhães, T. M.
(2025). Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile. Mathematics, 13(23), 3838.
https://doi.org/10.3390/math13233838
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