Published

2025-01-01

Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections

Modelado de valores extremos utilizando el proceso de poisson compuesto: predicción de la recaudación de multas por exceso de velocidad

DOI:

https://doi.org/10.15446/rce.v48n1.113610

Keywords:

Extreme value theory, Speeding violations, Compound Poisson process, Bayesian approach. (en)
Enfoque bayesiano, Infracciones por exceso de velocidad, Proceso de Poisson compuesto, Teoría de valores extremos.} (es)

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Authors

Speeding violations are intended as both punitive and educational actions for drivers who exceed the maximum allowed speed on the roads. From a tax collection perspective, they have a significant impact on the municipal budget. Extreme Value Theory has been a valuable tool for modeling the distribution of speeding violations. Additionally, it is equally important to model the daily number of speeding occurrences. A powerful method for jointly modeling both variables is the Compound Poisson Process. By understanding both speeding behavior and the number of infractions, we can estimate the expected value of total tax collections. A mixture of Gamma densities combining with the Generalized Pareto Distribution (GPD) in tail was proposed to model the distribution of speeding values. The results indicated significant potential for tax collection.

Las infracciones por exceso de velocidad están destinadas tanto a acciones punitivas como educativas para los conductores que superan la velocidad máxima permitida en las carreteras. Desde una perspectiva de recaudación fiscal, tienen un impacto significativo en el presupuesto municipal. La Teoría de Valores Extremos ha sido una herramienta valiosa para modelar la distribución de las infracciones por exceso de velocidad. Además, es igualmente importante modelar el número diario de estas infracciones. Un método poderoso para modelar ambas variables conjuntamente es el Proceso de Poisson Compuesto. Al comprender tanto el comportamiento de los conductores como el número de infracciones, podemos estimar el valor esperado de la recaudación total de impuestos. Se propuso una mezcla de densidades Gamma combinada con la Distribución Generalizada de Pareto (GPD, por sus siglas en inglés) en la cola para modelar la distribución de los valores de exceso de velocidad. Los resultados indicaron un potencial significativo para la recaudación fiscal.

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How to Cite

APA

Nascimento, F., S. Costa, F. M. and da Silva Ferraz, V. R. (2025). Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections. Revista Colombiana de Estadística, 48(1), 239–250. https://doi.org/10.15446/rce.v48n1.113610

ACM

[1]
Nascimento, F., S. Costa, F.M. and da Silva Ferraz, V.R. 2025. Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections. Revista Colombiana de Estadística. 48, 1 (Jan. 2025), 239–250. DOI:https://doi.org/10.15446/rce.v48n1.113610.

ACS

(1)
Nascimento, F.; S. Costa, F. M.; da Silva Ferraz, V. R. Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections. Rev. colomb. estad. 2025, 48, 239-250.

ABNT

NASCIMENTO, F.; S. COSTA, F. M.; DA SILVA FERRAZ, V. R. Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections. Revista Colombiana de Estadística, [S. l.], v. 48, n. 1, p. 239–250, 2025. DOI: 10.15446/rce.v48n1.113610. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/113610. Acesso em: 19 feb. 2025.

Chicago

Nascimento, Fernando, Filipe Mateus S. Costa, and Valmaria Rocha da Silva Ferraz. 2025. “Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections”. Revista Colombiana De Estadística 48 (1):239-50. https://doi.org/10.15446/rce.v48n1.113610.

Harvard

Nascimento, F., S. Costa, F. M. and da Silva Ferraz, V. R. (2025) “Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections”, Revista Colombiana de Estadística, 48(1), pp. 239–250. doi: 10.15446/rce.v48n1.113610.

IEEE

[1]
F. Nascimento, F. M. S. Costa, and V. R. da Silva Ferraz, “Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections”, Rev. colomb. estad., vol. 48, no. 1, pp. 239–250, Jan. 2025.

MLA

Nascimento, F., F. M. S. Costa, and V. R. da Silva Ferraz. “Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections”. Revista Colombiana de Estadística, vol. 48, no. 1, Jan. 2025, pp. 239-50, doi:10.15446/rce.v48n1.113610.

Turabian

Nascimento, Fernando, Filipe Mateus S. Costa, and Valmaria Rocha da Silva Ferraz. “Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections”. Revista Colombiana de Estadística 48, no. 1 (January 21, 2025): 239–250. Accessed February 19, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/113610.

Vancouver

1.
Nascimento F, S. Costa FM, da Silva Ferraz VR. Extreme Value Modeling with the Compound Poisson Process: Predicting Speeding Fine Collections. Rev. colomb. estad. [Internet]. 2025 Jan. 21 [cited 2025 Feb. 19];48(1):239-50. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/113610

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