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

References

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How to Cite

APA

Omair, M. A., AlMuhayfith, F. E. and Alzaid, A. A. (2018). A Bivariate Model based on Compound Negative Binomial Distribution. Revista Colombiana de Estadística, 41(1), 87–108. https://doi.org/10.15446/rce.v41n1.57803

ACM

[1]
Omair, M.A., AlMuhayfith, F.E. and Alzaid, A.A. 2018. A Bivariate Model based on Compound Negative Binomial Distribution. Revista Colombiana de Estadística. 41, 1 (Jan. 2018), 87–108. DOI:https://doi.org/10.15446/rce.v41n1.57803.

ACS

(1)
Omair, M. A.; AlMuhayfith, F. E.; Alzaid, A. A. A Bivariate Model based on Compound Negative Binomial Distribution. Rev. colomb. estad. 2018, 41, 87-108.

ABNT

OMAIR, M. A.; ALMUHAYFITH, F. E.; ALZAID, A. A. A Bivariate Model based on Compound Negative Binomial Distribution. Revista Colombiana de Estadística, [S. l.], v. 41, n. 1, p. 87–108, 2018. DOI: 10.15446/rce.v41n1.57803. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/57803. Acesso em: 25 apr. 2024.

Chicago

Omair, Maha Ahmad, Fatimah E AlMuhayfith, and Abdulhamid A Alzaid. 2018. “A Bivariate Model based on Compound Negative Binomial Distribution”. Revista Colombiana De Estadística 41 (1):87-108. https://doi.org/10.15446/rce.v41n1.57803.

Harvard

Omair, M. A., AlMuhayfith, F. E. and Alzaid, A. A. (2018) “A Bivariate Model based on Compound Negative Binomial Distribution”, Revista Colombiana de Estadística, 41(1), pp. 87–108. doi: 10.15446/rce.v41n1.57803.

IEEE

[1]
M. A. Omair, F. E. AlMuhayfith, and A. A. Alzaid, “A Bivariate Model based on Compound Negative Binomial Distribution”, Rev. colomb. estad., vol. 41, no. 1, pp. 87–108, Jan. 2018.

MLA

Omair, M. A., F. E. AlMuhayfith, and A. A. Alzaid. “A Bivariate Model based on Compound Negative Binomial Distribution”. Revista Colombiana de Estadística, vol. 41, no. 1, Jan. 2018, pp. 87-108, doi:10.15446/rce.v41n1.57803.

Turabian

Omair, Maha Ahmad, Fatimah E AlMuhayfith, and Abdulhamid A Alzaid. “A Bivariate Model based on Compound Negative Binomial Distribution”. Revista Colombiana de Estadística 41, no. 1 (January 1, 2018): 87–108. Accessed April 25, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/57803.

Vancouver

1.
Omair MA, AlMuhayfith FE, Alzaid AA. A Bivariate Model based on Compound Negative Binomial Distribution. Rev. colomb. estad. [Internet]. 2018 Jan. 1 [cited 2024 Apr. 25];41(1):87-108. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/57803

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CrossRef citations4

1. Bing Su, Fukang Zhu. (2021). Comparison of BINAR(1) models with bivariate negative binomial innovations and explanatory variables. Journal of Statistical Computation and Simulation, 91(8), p.1616. https://doi.org/10.1080/00949655.2020.1863965.

2. Q Ferré, G Charbonnier, N Sadouni, F Lopez, Y Kermezli, S Spicuglia, C Capponi, B Ghattas, D Puthier, Bonnie Berger. (2020). OLOGRAM: determining significance of total overlap length between genomic regions sets. Bioinformatics, 36(6), p.1920. https://doi.org/10.1093/bioinformatics/btz810.

3. Tran Loc Hung, Phan Tri Kien. (2021). On the Order of Approximation in Limit Theorems for Negative–Binomial Sums of Strictly Stationary m-Dependent Random Variables. Acta Mathematica Vietnamica, 46(1), p.203. https://doi.org/10.1007/s40306-020-00406-x.

4. Dodi Devianto, Stefi Amalia Fitri, Hazmira Yoza, Maiyastri Maiyastri. (2022). The Infinite Divisibility of Compound Negative Binomial Distribution as the Sum of Laplace Distribution. Pakistan Journal of Statistics and Operation Research, , p.395. https://doi.org/10.18187/pjsor.v18i2.2767.

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