Publicado

2020-01-01

Two Useful Discrete Distributions to Model Overdispersed Count Data

Dos distribuciones discretas útiles para modelar datos de recuento sobredispersos

DOI:

https://doi.org/10.15446/rce.v43n1.77052

Palabras clave:

Discretization methods, Shanker distribution, overdispersion, maximum likelihood estimation, simulation study (en)
Estimación de máxima verosimilitud, Distribuciones discretas, Distribución de Shanker, Simulación del Monte Carlo, Sobredispersión (es)

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Autores/as

The methods to obtain discrete analogues of continuous distributions have been widely considered in recent years. In general, the discretization process provides probability mass functions that can be competitive with the traditional model used in the analysis of count data, the Poisson distribution. The discretization procedure also avoids the use of continuous distribution in the analysis of strictly discrete data. In this paper, we seek to introduce two discrete analogues for the Shanker distribution using the method of the infinite series and the method based on the survival function as alternatives to model overdispersed datasets. Despite the difference between discretization methods, the resulting distributions are interchangeable. However, the distribution generated by the method of infinite series method has simpler mathematical expressions for the shape, the generating functions and the central moments. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is carried out in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed models is evaluated using real datasets provided by the literature.
Los métodos para obtener análogos discretos de distribuciones continuas han sido ampliamente considerados en los últimos años. En general, el proceso de discretización proporciona funciones de probabilidad en masa que pueden ser competitivas con el modelo tradicional utilizado en el análisis de datos de conteo, la distribución de Poisson. El procedimiento de discretización también evita el uso de la distribución continua en el análisis de datos estrictamente discretos. En este artículo, intentamos introducir dos análogos discretos para la distribución de Shanker utilizando el método de la serie infinita y el método basado en la función de supervivencia como alternativas para modelar conjuntos de datos sobre dispersados. A pesar de la diferencia entre los métodos de discretización, las distribuciones resultantes son intercambiables. Sin embargo, la distribución generada por el método del método de series infinitas tiene expresiones matemáticas más simples para la forma, las funciones de generación y los momentos centrales. La teoría de máxima verosimilitud se considera para la estimación y las preocupaciones de inferencia asintótica. Se lleva a cabo un estudio de simulación para evaluar algunas propiedades frecuentistas de la metodología desarrollada. La utilidad de los modelos propuestos se evalúa utilizando conjuntos de datos reales proporcionados por la literatura.

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Cómo citar

APA

Mazucheli, J., Bertoli, W. y Oliveira, R. P. (2020). Two Useful Discrete Distributions to Model Overdispersed Count Data. Revista Colombiana de Estadística, 43(1), 21–48. https://doi.org/10.15446/rce.v43n1.77052

ACM

[1]
Mazucheli, J., Bertoli, W. y Oliveira, R.P. 2020. Two Useful Discrete Distributions to Model Overdispersed Count Data. Revista Colombiana de Estadística. 43, 1 (ene. 2020), 21–48. DOI:https://doi.org/10.15446/rce.v43n1.77052.

ACS

(1)
Mazucheli, J.; Bertoli, W.; Oliveira, R. P. Two Useful Discrete Distributions to Model Overdispersed Count Data. Rev. colomb. estad. 2020, 43, 21-48.

ABNT

MAZUCHELI, J.; BERTOLI, W.; OLIVEIRA, R. P. Two Useful Discrete Distributions to Model Overdispersed Count Data. Revista Colombiana de Estadística, [S. l.], v. 43, n. 1, p. 21–48, 2020. DOI: 10.15446/rce.v43n1.77052. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/77052. Acesso em: 5 ago. 2024.

Chicago

Mazucheli, Josmar, Wesley Bertoli, y Ricardo Puziol Oliveira. 2020. «Two Useful Discrete Distributions to Model Overdispersed Count Data». Revista Colombiana De Estadística 43 (1):21-48. https://doi.org/10.15446/rce.v43n1.77052.

Harvard

Mazucheli, J., Bertoli, W. y Oliveira, R. P. (2020) «Two Useful Discrete Distributions to Model Overdispersed Count Data», Revista Colombiana de Estadística, 43(1), pp. 21–48. doi: 10.15446/rce.v43n1.77052.

IEEE

[1]
J. Mazucheli, W. Bertoli, y R. P. Oliveira, «Two Useful Discrete Distributions to Model Overdispersed Count Data», Rev. colomb. estad., vol. 43, n.º 1, pp. 21–48, ene. 2020.

MLA

Mazucheli, J., W. Bertoli, y R. P. Oliveira. «Two Useful Discrete Distributions to Model Overdispersed Count Data». Revista Colombiana de Estadística, vol. 43, n.º 1, enero de 2020, pp. 21-48, doi:10.15446/rce.v43n1.77052.

Turabian

Mazucheli, Josmar, Wesley Bertoli, y Ricardo Puziol Oliveira. «Two Useful Discrete Distributions to Model Overdispersed Count Data». Revista Colombiana de Estadística 43, no. 1 (enero 1, 2020): 21–48. Accedido agosto 5, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/77052.

Vancouver

1.
Mazucheli J, Bertoli W, Oliveira RP. Two Useful Discrete Distributions to Model Overdispersed Count Data. Rev. colomb. estad. [Internet]. 1 de enero de 2020 [citado 5 de agosto de 2024];43(1):21-48. Disponible en: https://revistas.unal.edu.co/index.php/estad/article/view/77052

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CrossRef citations1

1. Md Mahadi Hasan, K. Krishnamoorthy. (2023). Confidence intervals and prediction intervals for two-parameter negative binomial distributions. Journal of Applied Statistics, , p.1. https://doi.org/10.1080/02664763.2023.2297157.

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