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## Print version ISSN 0120-1751

### Rev.Colomb.Estad. vol.41 no.1 Bogotá Jan./June 2018

#### http://dx.doi.org/10.15446/rce.v41n1.57803

Artículos originales de investigación

A Bivariate Model based on Compound Negative Binomial Distribution

Maha Omair1  a  , Fatimah Almuhayfith2  b  , Abdulhamid Alzaid1  c

1Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh, Saudi Arabia.

2Department of Mathematics and Statistics, College of Sciences, King Faisal University, Alahsa, Saudi Arabia.

Abstract

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.

Key words: Bivariate distribution; Compound distribution; Correlation coefficient; Divisibility; Geometric distribution; Moments; Negative binomial distribution; Total positivity

Resumen

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.

Palabras-clave: coeficiente de correlación; distribución binomial negativa; distribución bivariada; distribución compuesto; distribución geométrica; divisibilidad; momentos; positividad total

Full text available only in PDF format.

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