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Introducing the Discrete xLindley Distribution: A One-Parameter Model for Overdispersed Data
La distribución discreta de xLindley: un modelo de un parámetro para datos sobredispersos
DOI:
https://doi.org/10.15446/rce.v48n1.115319Keywords:
Count data, Discretization methods, xLindley distribution, Data dispersion, Bayesian inference, Simulation study. (en)Datos de recuento, Métodos de discretización, Distribución xLindley, Dispersión de datos, Inferencia bayesiana, Estudio de simulación. (es)
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In this paper, we propose a new discrete model, the discrete analog of the xLindley distribution, as an alternative for modeling overdispersed data. The model was derived using the method of infinite series, allowing us to capture complex characteristics of the data, and its properties were studied in detail. Asymptotic results are presented to validate the model parameter estimates consistency in large samples. Additionally, a Bayesian approach was considered for inference with complete and right-censored data. The performance of the Bayesian estimators was evaluated through Monte Carlo simulations, enabling a comprehensive comparison of the effectiveness and efficiency of the estimators under different scenarios. The proposed model was applied to two real datasets, demonstrating its practical utility. The practical application included the analysis of discrete events in research environments, highlighting the model's flexibility in various situations. Furthermore, a comparison with other discrete distributions was provided, showcasing the advantages of the xLindley model over existing alternatives.
En este artículo, proponemos un nuevo modelo discreto, el análogo discreto de la distribución xLindley, como una alternativa para modelar datos sobredispersos. El modelo fue derivado utilizando el método de series infinitas, lo que nos permite capturar características complejas de los datos, y se estudiaron en detalle sus propiedades. Se presentan resultados asintóticos para validar la consistencia del modelo en grandes muestras. Además se consideró un enfoque bayesiano para la inferencia con datos completos y censurados a la derecha. El rendimiento de los estimadores bayesianos se evaluó a través de simulaciones de Monte Carlo, lo que permitió una comparación integral de la efectividad y eficiencia de los estimadores en diferentes escenarios. El modelo propuesto se aplicó a dos conjuntos de datos reales, demostrando su utilidad práctica. La aplicación práctica incluyó el análisis de eventos discretos en entornos de investigación, destacando la flexibilidad del modelo en diversas situaciones. Además, se proporcionó una comparación con otras distribuciones discretas, mostrando las ventajas del modelo xLindley sobre alternativas existentes.
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