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

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.

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.         [ Links ]

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

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.         [ Links ]

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

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

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

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

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.         [ Links ]

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

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

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.         [ Links ]

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.         [ Links ]

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