Published

2018-01-01

A Bivariate Model based on Compound Negative Binomial Distribution

Un modelo basado en bivariadas compuesto distribuci\'{o}n binomial negativa

DOI:

https://doi.org/10.15446/rce.v41n1.57803

Keywords:

bivariate distribution, Compound distribution, Negative binomial, Divisibility, Geometric distribution, Moments, Correlation coefficient, Total positivity.National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and (en)
coeficiente de correlación, distribución binomial negativa, distribución bivariada, distribución compuesto, distribución geométrica, divisibilidad, momentos, positividad total (es)

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Authors

  • Maha Ahmad Omair Assistant Professor of Statistics King Saud University
  • Fatimah E AlMuhayfith Assistant Professor of Statistics King Faisal University
  • Abdulhamid A Alzaid Professor of Statistics King Saud University

A new bivariate model is introduced by compounding negative binomial and geometric distributions. Distributional properties, including joint, marginal and conditional distributions are discussed. Expressions for the product moments, covariance and correlation coefficient are obtained. Some properties such as ordering, unimodality, monotonicity and self-decomposability are studied. Parameter estimators using the method of moments and maximum likelihood are derived. Applications to traffic accidents data are illustrated.

Un nuevo modelo de dos variables se introduce mediante la composición distribuciones binomiales negativos y geométricos. propiedades distributivas, incluyendo distribuciones conjuntas, marginales y condicionales se discuten. se obtienen las expresiones para los momentos de productos, la covarianza y el coeficiente de correlación. Se estudian algunas propiedades tales como pedidos, unimodalidad, monotonía y la auto-decomposability. estimadores de parámetros utilizando el método de los momentos y de máxima verosimilitud se derivan. Aplicaciones a los datos de accidentes de tráfico se ilustran

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