New classes of discrete bivariate distributions with application to football data

References

• Ahooyi, T.M., Arbogast, J.E., Oktem, U. G., Seider, W. D. and Soroush, M. (2014). Estimation of complete discrete multivariate probability distributions from scarce data with application to risk assessment and fault detection. Ind. Eng. Chem. Res. 53:7538–7547.
   Web of Science ®Google Scholar
• Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Autom. Control 19:716–723.
   Web of Science ®Google Scholar
• Antony, D., Jayakumar, K. (2013). Bivariate discrete Linnik distribution. Statistica.
   Google Scholar
• Bairamov, I., Gultekin, O.E. (2010). Discrete distributions connected with the bivariate binomial. Hacettepe J. Math. Stat. 39:109–120.
   Web of Science ®Google Scholar
• Becker, N.G., Utev, S. (2002). Multivariate discrete distributions with a product-type dependence. J. Multivariate Anal. 83:509–524.
   Web of Science ®Google Scholar
• Burnham, K.P., Anderson, D.R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociol. Methods Res. 33:261–304.
   Web of Science ®Google Scholar
• Cacoullos, T., Papageorgiou, H. (2012). On bivariate discrete distributions generated by compounding. In: Taillie, C., Patil, G.P., Baldessari, B.A., eds. Statistical Distributions in Scientific Work, volume 4, Models, Structures, and Characterizations.
   Google Scholar
• Fang, Y. (2011). Asymptotic equivalence between cross-validations and Akaike Information Criteria in mixed-effects models. J. Data Sci. 9:15–21.
   Google Scholar
• Garrido, L.R., Birchmeier, A.N., Munilla, S., Cantet, R.J.C. (2008). Estimation of effective population size using bivariate discrete distributions for modeling family size in beef cattle. Livestock Sci. 117:43–51.
   Web of Science ®Google Scholar
• Gomez-Deniz, E., Sarabia, J.M., Balakrishnan, N. (2012). A multivariate discrete Poisson-Lindley distribution: Extensions and actuarial applications. ASTIN Bull. 42:655–678.
   Web of Science ®Google Scholar
• He, Q.-M., Ren, J. (2015). Parameter estimation of discrete multivariate phase-type distributions. Methodol. Comput. Appl. Probab. doi:10.1007/s11009-015-9442-y.
   Web of Science ®Google Scholar
• Holgate, B. (1964). Estimation for the bivariate Poisson distribution. Biometrika 51:241–245.
   Web of Science ®Google Scholar
• Hoshino, N. (2006). A discrete multivariate distribution resulting from the law of small numbers. J. Appl. Probab. 43:852–866.
   Web of Science ®Google Scholar
• Ip, E.H., Wang, Y.J. (2009). Canonical representation of conditionally specified multivariate discrete distributions. J. Multivariate Anal. 100:1282–1290.
   Web of Science ®Google Scholar
• Johnson, N.L., Kotz, S., Balakrishnan, N. (1997). Discrete Multivariate Distributions. New York: John Wiley and Sons.
   Google Scholar
• Kumar, C.S. (2007). A unified approach to bivariate discrete distributions. Metrika 67:113–123.
   Web of Science ®Google Scholar
• Lee, H., Cha, J.H. (2015). On two general classes of discrete bivariate distributions. Am. Stat. 69:221–230.
   Web of Science ®Google Scholar
• McHale, I., Scarf, P. (2007). Modelling soccer matches using bivariate discrete distributions with general dependence structure. Stat. Neerlandica 61:432–445.
   Web of Science ®Google Scholar
• McHale, I., Scarf, P. (2011). Modelling the dependence of goals scored by opposing teams in international soccer matches. Stat. Modell. 11:219–236.
   Web of Science ®Google Scholar
• Miethe, T.D., Hart, T.C., Regoeczi, W.C. (2008). The conjunctive analysis of case configurations: An exploratory method for discrete multivariate analyses of crime data. J. Quant. Criminol. 24:227–241.
   Web of Science ®Google Scholar
• Nikoloulopoulos, A.K. (2013). Copula-based models for multivariate discrete response data. In: Copulae in Mathematical and Quantitative Finance, Volume 213 of the Series Lecture Notes in Statistics (pp. 231–249).
   Google Scholar
• Nikulin, M.S., Smirnovc, T.I., Voinov, V.G. (2002). Multivariate discrete distributions induced by an urn scheme, linear diophantine equations, unbiased estimating, testing and applications. J. Stat. Plann. Inference 101:255–266.
   Web of Science ®Google Scholar
• Ong, S.H., Ng, C.M. (2013). A bivariate generalization of the noncentral negative binomial distribution. Commun. Stat. — Simul. Comput. 42:570–585.
   Web of Science ®Google Scholar
• Ozel, G. (2011a). A bivariate compound Poisson model for the occurrence of foreshocks and aftershock sequences in Turkey. Environmetrics 22:847–856.
   Web of Science ®Google Scholar
• Ozel, G. (2011b). On certain properties of a class of bivariate compound Poisson distributions and an application on earthquake data. Revista Colombiana de Estadistica 34:545–566.
   Google Scholar
• Ozel, G. (2013). On the moment characteristics of univariate compound Poisson and bivariate compound Poisson processes with applications. Revista Colombiana Estadistica 36:59–77.
   Google Scholar
• Panagiotelis, A., Czado, C., Joe, H. (2012). Pair copula constructions for multivariate discrete data. J. Am. Stat. Assoc. 107:1063–1072.
   Web of Science ®Google Scholar
• Piperigou, V.E., Papageorgiou, H. (2003). On truncated bivariate discrete distributions: A unified treatment. Metrika 58:221–233.
   Web of Science ®Google Scholar
• R Development Core Team. (2015). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Reilly, C.H., Sapkota, N. (2015). A family of composite discrete bivariate distributions with uniform marginals for simulating realistic and challenging optimization-problem instances. Eur. J. Oper. Res. 241:642–652.
   Web of Science ®Google Scholar
• Schwarz, G.E. (1978). Estimating the dimension of a model. Ann. Stat. 6:461–464.
   Web of Science ®Google Scholar
• Tonda, T. (2005). A class of multivariate discrete distributions based on an approximate density in GLMM. Hiroshima Math. J. 35:327–349.
   Google Scholar