A skew integer-valued time-series process with generalized Poisson difference marginal distribution

References

• Al-Nachawati, H., I. Alwasel, and A. A. Alzaid. 1997. Estimating the parameters of the generalized Poisson AR(1) process. Journal of Statistical Computation and Simulation 56:337–52. doi:10.1080/00949659708811798.
   Web of Science ®Google Scholar
• Al-Osh, M. A., and A. A. Alzaid. 1987. First order integer-valued autoregressive INAR(1) process. Journal of Time Series Analysis 8:261–75. doi:10.1111/j.1467-9892.1987.tb00438.x.
   Google Scholar
• Alzaid, A. A., and M. Al-Osh. 1990. An integer-valued p th-order autoregressive structure (INAR(p)) process. Journal of Applied Probability 27:314–24. doi:10.2307/3214650.
   Web of Science ®Google Scholar
• Alzaid, A. A., and M. A. Al-Osh. 1993. Some autoregressive moving average processes with generalized Poisson marginal distributions. Annals of the Institute of Mathematical Statistics 45:223–32. doi:10.1007/BF00775809.
   Web of Science ®Google Scholar
• Alzaid, A. A., and M. A. Omair. 2014. Poisson difference integer valued autoregressive model of order one. Bulletin of the Malaysian Mathematical Sciences Society 37:465–85.
   Web of Science ®Google Scholar
• Barreto-Souza, W., and M. Bourguignon. 2015. A skew true INAR(1) process with application. AStA - Advances in Statistical Analysis 99:189–208. doi:10.1007/s10182-014-0236-2.
   Web of Science ®Google Scholar
• Bourguignon, M., and K. L. Vasconcellos. 2016. A new skew integer valued time series process. Statistical Methodology 31:8–19. doi:10.1016/j.stamet.2016.01.002.
   Google Scholar
• Chesneau, C., and M. Kachour. 2012. A parametric study for the first-order signed integer-valued autoregressive process. Journal of Statistical Theory and Practice 6:760–82. doi:10.1080/15598608.2012.719816.
   Google Scholar
• Consul, P. C. 1974. A simple urn model dependent upon predetermined strategy. Sankhyā: the Indian Journal of Statistics. Series B 36:391–99.
   Google Scholar
• Consul, P. C. 1975. On a characterization of Lagrangian Poisson and quasi-binomial distributions. Communications in Statistics-Theory and Methods 4:555–63.
   Web of Science ®Google Scholar
• Consul, P. C. 1986. On the differences of two generalized Poisson variates. Communications in Statistics - Simulation and Computation 15:761–67. doi:10.1080/03610918608812538.
   Web of Science ®Google Scholar
• Consul, P. C. 1989. Generalized Poisson distribution: Properties and applications. New York: Marcel Dekker Inc.
   Google Scholar
• Consul, P. C. 1990. On some properties and applications of quasi-binomial distribution. Communications in Statistics - Theory and Methods 19:477–504. doi:10.1080/03610929008830214.
   Web of Science ®Google Scholar
• Consul, P. C., and F. Famoye. 2006. Lagrangian probability distributions. Boston: Birkhäuser.
   Google Scholar
• Consul, P. C., and G. C. Jain. 1973. A generalization of Poisson distribution. Technometrics 15:791–99. doi:10.1080/00401706.1973.10489112.
   Web of Science ®Google Scholar
• Consul, P. C., and S. P. Mittal. 1975. A new urn model with predetermined strategy. Biometrical Journal 17:67–75.
   Web of Science ®Google Scholar
• Du, J., and Y. Li. 1991. The integer valued autoregressive (INAR(P)) model. Times Series Analysis Journal 12:129–42. doi:10.1111/j.1467-9892.1991.tb00073.x.
   Google Scholar
• Fazal, S. S. 1976. A test for quasi-binomial distribution. Biom Journal 18:619–22. doi:10.1002/(ISSN)1521-4037.
   Google Scholar
• Freeland, R. K. 2010. True integer value time series. Advancement Statistical Analysis 94:217–29. doi:10.1007/s10182-010-0135-0.
   Web of Science ®Google Scholar
• Joe, H., and R. Zhu. 2005. Generalized Poisson distribution: The property of mixture of Poisson and comparison with negative-binomial distribution. Biometrical Journal 47:219–29. doi:10.1002/bimj.200410102.
   PubMed Web of Science ®Google Scholar
• Johnson, N. L., S. Kotz, and A. W. Kemp. 2005. Univariate discrete distributions, 3rd ed. New York: John Wiley & Sons, Inc.
   Google Scholar
• Karlis, D., and I. Ntzoufras. 2006. Bayesian analysis of the differences of count data. Medical Statistics 25:1885–905. doi:10.1002/(ISSN)1097-0258.
   PubMed Web of Science ®Google Scholar
• Klimko, L. A., and P. I. Nelson. 1978. On conditional least squares estimation for stochastic processes. The Annals of Statistics 629–42. doi:10.1214/aos/1176344207.
   Web of Science ®Google Scholar
• Korwar, R. M. 1977. On characterizing lagrangian poisson and quasi-binomial distributions. Communications in Statistics - Theory and Methods 6:1409–15. doi:10.1080/03610927708827583.
   Web of Science ®Google Scholar
• Nastić, A. S., M. M. Ristić, and M. S. Djordjević. 2016. An INAR model with discrete laplace marginal distributions. Brazilian Journal of Probability and Statistics 30:107–26. doi:10.1214/14-BJPS262.
   Web of Science ®Google Scholar
• Ristić, M. M., H. S. Bakouch, and A. S. Nastić. 2009. A new geometric first-order integer-valued autoregressive(NGINAR(1)) process. Journal of Statistical Planning and Inference 139:2218–26. doi:10.1016/j.jspi.2008.10.007.
   Web of Science ®Google Scholar
• Shahtahmassebi, G., and R. Moyeed. 2014. Bayesian modelling of integer data using the generalized Poisson difference distribution. International Journal of Statistics and Probability 3:35–48. doi:10.5539/ijsp.v3n1p35.
   Google Scholar
• Shahtahmassebi, G., and R. Moyeed. 2016. An application of the generalized Poisson difference distribution to the Bayesian modelling of football scores. Statistica Neerlandica 70:260–73. doi:10.1111/stan.v70.3.
   Web of Science ®Google Scholar
• Shenton, L. R. 2006. Quasibinomial distributions. Encyclopedia of Statistical Sciences 10:6744–46.
   Google Scholar
• Steutel, F. W., and K. Van Harn. 1979. Discrete analogues of self-decomposability and stability. The Annals of Probability 7:893–99. doi:10.1214/aop/1176994950.
   Web of Science ®Google Scholar
• Weiß, C. H. 2008. Thinning operations for modeling time series of counts-a survey. AStA Advances in Statistical Analysis 92:319–41. doi:10.1007/s10182-008-0072-3.
   Web of Science ®Google Scholar