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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.1 Bogotá Jan./June 2020 Epub June 05, 2020
https://doi.org/10.15446/rce.v43n1.77052
ARTÍCULOS ORIGINALES DE INVESTIGACIÓN
Two Useful Discrete Distributions to Model Overdispersed Count Data
Dos distribuciones discretas útiles para modelar datos de recuento sobredispersos
1 Department of Statistics, State University of Maringá, Maringá, Brazil. PhD. E-mail: jmazucheli@gmail.com
2Department of Statistics, Federal University of Technology - Paraná, Curitiba, Brazil. PhD. E-mail: wbsilva@utfpr.edu.br
3 Medical School of Ribeirão Preto, University of São Paulo, Ribeirão Preto, Brazil. PhD. E-mail: rpuziol.oliveira@gmail.com
The methods to obtain discrete analogs 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 tra ditional 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 analogs for the Shanker distribution using the method of the in finite 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 dis tribution generated by the method of the infinite series method has simpler mathematical expressions for the shape, the generating functions, and the central moments. The maximum likelihood theory is considered for estima tion 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 pro vided by the literature.
Key words: Maximum likelihood estimation; Discrete distributions; Monte Carlo simulation; Overdispersion; Shanker distribution
Los métodos para obtener análogos discretos de distribuciones continuas han sido ampliamente considerados en los últimos años. En general, el pro ceso 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 al ternativas 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 de series infinitas tiene expresiones matemáticas más simples para la forma, las funciones de generación y los momentos centrales. La teoría de máxi ma 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 utili dad de los modelos propuestos se evalúa utilizando conjuntos de datos reales proporcionados por la literatura.
Palabras clave: Estimación de máxima verosimilitud; Distribuciones disc retas; Distribución de Shanker; Simulación del Monte Carlo; Sobredispersión
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