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Modelado de las proporciones con puntos finales excesivos basado en un modelo binomial generalizado de Lindley

Dianliang Deng1, Xiaoqing Zhang1

  • 1Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina, S4S 0A2 SK Canada.

Journal of statistical theory and applications : JSTA
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Resumen

Una nueva distribución binomial generalizada de Lindley (GLB) modela eficazmente datos proporcionales con problemas en los puntos finales. Este modelo estadístico flexible ofrece un análisis mejorado para diversas dispersiones y formas de datos.

Palabras clave:
regresión binomialalgoritmo EMinflación de puntos finalesdistribución de Lindleyproporcionesresiduos de cuantiles aleatorizados

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Área de la Ciencia:

  • Estadística
  • Teoría de la Probabilidad
  • Modelado Estadístico

Sus antecedentes:

  • Los datos proporcionales a menudo presentan observaciones excesivas en los puntos finales (0 o 1).
  • Los modelos binomiales existentes pueden no capturar adecuadamente estos fenómenos de puntos finales o los niveles de dispersión variables.
  • Se necesitan distribuciones estadísticas novedosas para el análisis flexible de dichos datos.

Objetivo del estudio:

  • Introducir la distribución binomial generalizada de Lindley (GLB).
  • Desarrollar métodos de inferencia estadística para el modelo GLB, incluida la regresión.
  • Evaluar el rendimiento y la utilidad práctica del modelo GLB.

Principales métodos:

  • La distribución GLB se construye combinando la distribución binomial con una distribución generalizada de Lindley de tres parámetros.
  • Se derivan las propiedades probabilísticas (PMF, momentos, media, varianza, MGF, índice de dispersión).
  • La inferencia basada en la verosimilitud se implementa utilizando los algoritmos de Fisher scoring y Expectation-Maximization (EM), incluido un EM penalizado para la estabilidad.
  • El diagnóstico del modelo utiliza residuos de Pearson, de deviance y de cuantiles aleatorizados.

Principales resultados:

  • La distribución GLB demuestra flexibilidad en el modelado de datos subdispersos y sobré-dispersos, así como formas unimodales y bimodales.
  • Los estudios de simulación confirman el rendimiento de los procedimientos de estimación.
  • El modelo de regresión GLB proporciona un ajuste superior al conjunto de datos de moscas blancas en comparación con los modelos existentes.

Conclusiones:

  • La distribución binomial generalizada de Lindley es una nueva herramienta valiosa para analizar datos proporcionales, especialmente con inflación de puntos finales.
  • Los métodos de inferencia desarrollados, incluido el EM penalizado, son eficaces para la estimación de parámetros.
  • El modelo de regresión GLB ofrece un rendimiento mejorado para el análisis de datos proporcionales del mundo real.