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Original Articles

The Touchard distribution

ORCID Icon, ORCID Icon, , ORCID Icon & ORCID Icon
Pages 2049-2059 | Received 19 Mar 2016, Accepted 17 Feb 2018, Published online: 08 Mar 2018

References

  • Ahrens, J. H., and U. Dieter. 1982. Computer generation of Poisson deviates from modified normal distributions. ACM Trans. Math. Software 8:163–79.
  • Bardwell, G. E., and E. L. Crow. 1964. A two-parameter family of hyper-Poisson distributions. J. Amer. Statist. Assoc. 59:133–41.
  • Bhati, D., D. V. S. Sastry, and P. Z. Maha Qadri. 2015. A new generalized Poisson-Lindley distribution: Applications and properties. Austrian J. Statist. 44:35–51.
  • Böhning, D., E. Dietz, P. Schlattmann, L. Mendonça, and U. Kirchner. 1999. The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology. J. R. Stat. Soc. A 162:195–209.
  • Chakraborty, S. 2010. On some distributional properties of the family of weighted generalized Poisson distribution. Commum. Statist. Theor. Meth. 39:2767–88.
  • Chandra, N. K., D. Roy, and T. Ghosh. 2013. A generalized Poisson distribution. Commum. Statist. Theor. Meth. 33:94–107.
  • Chrysaphinou, O. 1985. On Touchard polynomials. Discrete Math. 54:143–52.
  • Consul, P. C., and G. C. Jain. 1973. A generalization of the Poisson distribution. Technometrics 15:791–99.
  • Dandekar, V. M. 1955. Certain modified forms of binomial and Poisson distributions. Sankhyā 15:237–50.
  • Fishman, G. 2003. Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer.
  • Gurmu, S. 1998. Generalized hurdle count data regression models. Econ. Lett. 58:263–68.
  • Hirotsu, N., and M. Wright. 2003. An evaluation of characteristics of teams in association football by using a Markov process model. J. R. Stat. Soc. D 52:591–602.
  • Johnson, N. L., A. W. Kemp, and S. Kotz. 2005. Univariate discrete distributions. New York: Wiley.
  • Kadane, J. B., G. Shmueli, T. P. Minka, S. Borle, and P. Boatwright. 2006. Conjugate analysis of the Conway-Maxwell-Poisson distribution. Bayesian Anal. 2:363–74.
  • Kumar, C. S., and B. U. Nair. 2012. An alternative hyper-Poisson distribution. Statistica 72:357–69.
  • Kumar, C. S., and D. S. Shibu. 2011. Modified intervened Poisson distribution. Statistica 71:489–99.
  • Lambert, D. 1992. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34:1–14.
  • Mullahy, J. 1986. Specification and testing of some modified count data models. J. Econometrics 33:341–65.
  • Panjer, H. H., and S. Wang. 1993. On the stability of recursive formulas. ASTIN Bull. 23:227–58.
  • Ridout, M. S., J. P. Hinde, and C. G. B. Demetrio. 2005. Models for count data with many zeros, in Proceedings of the 19th International Biometric Conference, 179–192, Cape Town.
  • Rota, G.-C. 1964. The number of partitions of a set. Amer. Math. Monthly 71:498–504.
  • Sankaran, M. 1970. The discrete Poisson-Lindley distribution. Biometrics 26:145–49.
  • Satterthwaite, F. E. 1942. Generalized poisson distribution. Ann. Math. Statist. 13:410–17.
  • Shmueli, G., T. P. Minka, J. B. Kadane, S. Borle, and P. Boatwright. 2005. A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution. J. R. Stat. Soc. C 54:127–42.
  • Skinner, G. K., and G. H. Freeman. 2008. Soccer matches as experiments: How often does the best team win? J. Appl. Stat. 36:1087–95.
  • Touchard, J. 1939. Sur les cycles des substitutions. Acta Math. 70:243–79.

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