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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.v43n1.77542
ARTÍCULOS ORIGINALES DE INVESTIGACIÓN
Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data
Modelo oculto de Markov de Poisson generalizado para datos de recuento sobredispersados o subdispersos
a Department of Statistics, St. Thomas College, Pala, India. PhD. E-mail: sthottom@gmail.com
b Department of Statistics, St. Thomas College, Pala, India. Research Scholar. E-mail: ambilystat06@gmail.com
The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.
Key words: EM algorithm; Generalized Poisson distribution; Hidden Markov Model; Overdispersion
El método estadístico más adecuado para explicar la dependencia serial en los datos de recuento de series de tiempo se basan en los modelos ocultos de Markov (HMM). Estos modelos suponen que las observaciones se generan a partir de un finito mezcla de distribuciones regidas por el principio de la cadena de Markov (MC). El modelo de Markov oculto de Poisson (P-HMM) puede ser el método ms utilizado para modelar las situaciones mencionadas anteriormente. Sin embargo, en el escenario de la vida real, este modelo no puede considerarse como la mejor opción. Teniendo en cuenta este hecho, nosotros, en este artículo, apostamos por la distribución generalizada de Poisson (GPD) para modelar datos de conteo. Este método puede rectificar la sobredispersión y subdispersión en el modelo de Poisson. Aqu desarrollamos Poisson generalizado Modelo de Markov oculto (GP-HMM) combinando GPD con HMM para modelando tales datos. Los resultados del estudio sobre datos simulados y una aplicación de datos reales, casos mensuales de leptospirosis en el estado de Kerala en South India, muestra buenas propiedades de convergencia, lo que demuestra que el GP-HMM Es un método mejor en comparación con P-HMM.
Palabras clave: Algoritmo EM; Distribución generalizada de Poisson; Modelo oculto de Markov; Sobredispersión
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