Published

2016-01-01

A Trinomial Difference Distribution

Una distribución de diferencia trinomial

DOI:

https://doi.org/10.15446/rce.v39n1.55131

Keywords:

Binomial Distribution, Discrete Distribution, Maximum Likelihood Estimate, Moment Estimate, Poisson Distribution, Trinomial Distribution (en)
Distribución binomial, Distribución discretos, Estimación de máxima verosimilitud, Momento estimar, Distribución de Poisson, Distribución binomial. (es)

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Authors

  • Maha A. Omair King Saud University, Riyadh, Saudi Arabia
  • Abdulhamid Alzaid King Saud University, Riyadh, Saudi Arabia
  • Omalsad Odhah Prince Sattam Bin Abdulaziz University, Hotat Bani Tamim, Saudi Arabia

A trinomial difference distribution is defined and its distributional properties are illustrated. This distribution present the binomial difference distribution as a special case. The moment estimators and maximum likelihood estimators of the trinomial difference distribution are compared via simulation study. Two applications are modeled with the trinomial difference distribution and compared with other possible distributions.

Una distribución de diferencia trinomial se define en este artículo así como sus propiedades distribucionales. Esta distribución cuenta con la distribución de diferencia binomial como un caso particular. Los estimadores de momentos y de máxima verosimilitud son comparados vía un estudio de simulación. Dos aplicaciones son modelados con la distribución diferencia trinomial y se comparan con otras distribuciones posibles.

A Trinomial Difference Distribution

Una distribución de diferencia trinomial

MAHA A. OMAIR1, ABDULHAMID ALZAID2, OMALSAD ODHAH3

1King Saud University, College of Sciences, Department of Statistics and Operations Research, Riyadh, Saudi Arabia. Assistant Professor. Email: maomair@ksu.edu.sa
2King Saud University, College of Sciences, Department of Statistics and Operations Research, Riyadh, Saudi Arabia. Professor. Email: Alzaid@ksu.edu.sa
3Prince Sattam Bin Abdulaziz University, College of Sciences and Humanities, Department of Mathematics, Hotat Bani Tamim, Saudi Arabia. Assistant Professor. Email: o.odhah@psau.edu.sa

Abstract

A trinomial difference distribution is defined and its distributional properties are illustrated. This distribution present the binomial difference distribution as a special case. The moment estimators and maximum likelihood estimators of the trinomial difference distribution are compared via simulation study. Two applications are modeled with the trinomial difference distribution and compared with other possible distributions.

Key words: Binomial Distribution, Discrete Distribution, Maximum Likelihood Estimate, Moment Estimate, Poisson Distribution, Trinomial Distribution.

Resumen

Una distribución de diferencia trinomial se define en este artículo así como sus propiedades distribucionales. Esta distribución cuenta con la distribución de diferencia binomial como un caso particular. Los estimadores de momentos y de máxima verosimilitud son comparados vía un estudio de simulación. Dos aplicaciones son modelados con la distribución diferencia trinomial y se comparan con otras distribuciones posibles.

Palabras clave: distribución binomial, distribución discretos, estimación de máxima verosimilitud, momento estimar, distribución de Poisson, distribución binomial.

Texto completo disponible en PDF

References

1. Alzaid, A. A. & Omair, M. A. (2010), 'On the poisson difference distribution inference and applications', Bulletin of the Malaysian Mathematical Sciences Society 8(33), 17-45.

2. Alzaid, A. A. & Omair, M. A. (2012), 'An extended binomial distribution with applications', Communications in Statistics-Theory and Methods 41(19), 3511-3527.

3. Alzaid, A. A. & Omair, M. A. (2014), 'Poisson difference integer valued autoregressive model of order one', Bulletin of the Malaysian Mathematical Sciences Society 2(37), 465-485.

4. Bakouch, H., Kachour, M. & Nadarajah, S. (2013), An extended Poisson distribution. Working paper or preprint. *https://hal.archives-ouvertes.fr/hal-00959426

5. Castro, G. de (1952), 'Note on differences of bernoulli and poisson variables', Portugaliae mathematica 11(4), 173-175.

6. Inusah, S. & Kozubowski, T. J. (2006), 'A discrete analogue of the laplace distribution', Journal of statistical planning and inference 136(3), 1090-1102.

7. Karlis, D. & Ntzoufras, I. (2006), 'Bayesian analysis of the differences of count data', Statistics in medicine 25(11), 1885-1905.

8. Karlis, D. & Ntzoufras, I. (2009), 'Bayesian modelling of football outcomes: using the skellam's distribution for the goal difference', IMA Journal of Management Mathematics 20(2), 133-145.

9. Kemp, A. W. (1997), 'Characterizations of a discrete normal distribution', Journal of Statistical Planning and Inference 63(2), 223-229.

10. Kotz, S., Johnson, N. & Kemp, A. (1992), Univariate Discrete Distributions, 2 edn, John Wiley & Sons, Inc., New York.

11. Ong, S., Shimizu, K. & Min Ng, C. (2008), 'A class of discrete distributions arising from difference of two random variables', Computational Statistics & Data Analysis 52(3), 1490-1499.

12. Skellam, J. G. (1946), 'The frequency distribution of the difference between two poisson variates belonging to different populations', Journal of the Royal Statistical Society. Series A 109(3), 296.

[Recibido en junio de 2014. Aceptado en febrero de 2015]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n1a01,
    AUTHOR  = {A. Omair, Maha and Alzaid, Abdulhamid and Odhah, Omalsad},
    TITLE   = {{A Trinomial Difference Distribution}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {1},
    pages   = {1-15}
}

References

Alzaid, A. A. & Omair, M. A. (2010), ‘On the poisson difference distribution inference and applications’, Bulletin of the Malaysian Mathematical Sciences Society 8(33), 17–45.

Alzaid, A. A. & Omair, M. A. (2012), ‘An extended binomial distribution with applications’, Communications in Statistics-Theory and Methods 41(19), 3511–3527.

Alzaid, A. A. & Omair, M. A. (2014), ‘Poisson difference integer valued autoregressive model of order one’, Bulletin of the Malaysian Mathematical Sciences Society 2(37), 465–485.

Bakouch, H., Kachour, M. & Nadarajah, S. (2013), An extended Poisson distribution. Working paper or preprint. *https://hal.archives-ouvertes.fr/hal-00959426

Castro, G. (1952), ‘Note on differences of bernoulli and poisson variables’, Portugaliae mathematica 11(4), 173–175.

Inusah, S. & Kozubowski, T. J. (2006), ‘A discrete analogue of the laplace distribution’, Journal of statistical planning and inference 136(3), 1090–1102.

Karlis, D. & Ntzoufras, I. (2006), ‘Bayesian analysis of the differences of count data’, Statistics in medicine 25(11), 1885–1905.

Karlis, D. & Ntzoufras, I. (2009), ‘Bayesian modelling of football outcomes: using the skellam’s distribution for the goal difference’, IMA Journal of Management Mathematics 20(2), 133–145.

Kemp, A. W. (1997), ‘Characterizations of a discrete normal distribution’, Journal of Statistical Planning and Inference 63(2), 223–229.

Kotz, S., Johnson, N. & Kemp, A. (1992), Univariate Discrete Distributions, 2 edn, John Wiley & Sons, Inc., New York.

Ong, S., Shimizu, K. & Min Ng, C. (2008), ‘A class of discrete distributions arising from difference of two random variables’, Computational Statistics & Data Analysis 52(3), 1490–1499.

Skellam, J. G. (1946), ‘The frequency distribution of the difference between two poisson variates belonging to different populations’, Journal of the Royal Statistical Society. Series A 109(3), 296.

How to Cite

APA

Omair, M. A., Alzaid, A. and Odhah, O. (2016). A Trinomial Difference Distribution. Revista Colombiana de Estadística, 39(1), 1–15. https://doi.org/10.15446/rce.v39n1.55131

ACM

[1]
Omair, M.A., Alzaid, A. and Odhah, O. 2016. A Trinomial Difference Distribution. Revista Colombiana de Estadística. 39, 1 (Jan. 2016), 1–15. DOI:https://doi.org/10.15446/rce.v39n1.55131.

ACS

(1)
Omair, M. A.; Alzaid, A.; Odhah, O. A Trinomial Difference Distribution. Rev. colomb. estad. 2016, 39, 1-15.

ABNT

OMAIR, M. A.; ALZAID, A.; ODHAH, O. A Trinomial Difference Distribution. Revista Colombiana de Estadística, [S. l.], v. 39, n. 1, p. 1–15, 2016. DOI: 10.15446/rce.v39n1.55131. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/55131. Acesso em: 28 mar. 2025.

Chicago

Omair, Maha A., Abdulhamid Alzaid, and Omalsad Odhah. 2016. “A Trinomial Difference Distribution”. Revista Colombiana De Estadística 39 (1):1-15. https://doi.org/10.15446/rce.v39n1.55131.

Harvard

Omair, M. A., Alzaid, A. and Odhah, O. (2016) “A Trinomial Difference Distribution”, Revista Colombiana de Estadística, 39(1), pp. 1–15. doi: 10.15446/rce.v39n1.55131.

IEEE

[1]
M. A. Omair, A. Alzaid, and O. Odhah, “A Trinomial Difference Distribution”, Rev. colomb. estad., vol. 39, no. 1, pp. 1–15, Jan. 2016.

MLA

Omair, M. A., A. Alzaid, and O. Odhah. “A Trinomial Difference Distribution”. Revista Colombiana de Estadística, vol. 39, no. 1, Jan. 2016, pp. 1-15, doi:10.15446/rce.v39n1.55131.

Turabian

Omair, Maha A., Abdulhamid Alzaid, and Omalsad Odhah. “A Trinomial Difference Distribution”. Revista Colombiana de Estadística 39, no. 1 (January 1, 2016): 1–15. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/55131.

Vancouver

1.
Omair MA, Alzaid A, Odhah O. A Trinomial Difference Distribution. Rev. colomb. estad. [Internet]. 2016 Jan. 1 [cited 2025 Mar. 28];39(1):1-15. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/55131

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CrossRef Cited-by

CrossRef citations5

1. Huaping Chen, Zifei Han, Fukang Zhu. (2025). A trinomial difference autoregressive process for the bounded ℤ‐valued time series. Journal of Time Series Analysis, 46(1), p.152. https://doi.org/10.1111/jtsa.12762.

2. Maha A. Omair, Ghadah A. Alomani, Abdulhamid A. Alzaid. (2022). Bivariate Distributions on Z2. Bulletin of the Malaysian Mathematical Sciences Society, 45(S1), p.425. https://doi.org/10.1007/s40840-022-01318-9.

3. Huaping Chen, Jiayue Zhang, Fukang Zhu. (2023). A trinomial difference autoregressive model and its applications. Stat, 12(1) https://doi.org/10.1002/sta4.596.

4. Huaping Chen. (2025). A novel bounded ℤ-valued autoregressive model with its application on crime data. Journal of Statistical Computation and Simulation, 95(2), p.408. https://doi.org/10.1080/00949655.2024.2427360.

5. Dimitris Karlis, Naushad Mamode Khan. (2023). Models for Integer Data. Annual Review of Statistics and Its Application, 10(1), p.297. https://doi.org/10.1146/annurev-statistics-032921-022516.

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