Count data distributions: Some characterizations with applications

Journal of the American Statistical Association

Volumn 101, Issue 473, 2006, Pages 332-340

  Puig, Pedro ^a   Valero, Jordi ^a,b  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Closed under addition; Exploratory data analysis; Exponential dispersion model; Mixed Poisson; Overdispersion; Stopped Poisson; Zero inflation

Indexed keywords

EID: 33645519649     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214505000000718     Document Type: Article

References (27)

1. Böhning, D. (1998), "Zero-Inflated Poisson Models and C.A.MAN: A Tutorial Collection of Evidence," Biometrical Journal, 40, 833-843.
2. Böhning, D., Schlattmann, P., and Lindsay, B. (1992), "Computer-Assisted Analysis of Mixtures (C.A.MAN): Statistical Algorithms," Biometrics, 48, 283-303.
3. Cameron, A. C., and Trivedi, P. K. (1998), Regression Analysis of Count Data, Cambridge, U.K.: Cambridge University Press.
4. 2 Tests," Biometrics, 10, 417-451.
5. Collins, B. J., and Margolin, B. H. (1985), "Testing Goodness of Fit for the Poisson Assumption When Observations Are Not Identically Distributed," Journal of the American Statistical Association, 80, 411-418.
6. Douglas, J. B. (1980), Analysis With Standard Contagious Distributions, Fairland, MD: International Cooperative Publishing.
7. Feller, W. (1967), An Introduction to Probability Theory, Vol. I., New York: Wiley.
8. Gossiaux, A., and Lemaire, J. (1981), "Methodes d'Ajustement de Distributions de Sinistres," Bulletin of the Association of Swiss Actuaries, 81, 87-95.
9. Gupta, R. P., and Jain, G. C. (1974), "A Generalized Hermite Distribution and Its Properties," SIAM Journal of Applied Mathematics, 27, 359-363.
10. Hougaard, P., Ting Lee, M. L., and Whitmore, G. A. (1997), "Analysis of Overdispersed Count Data by Mixtures of Poisson Variables and Poisson Processes," Biometrics, 53, 1225-1238.
11. Hürlimann, W. (1992), "On Parameter Orthogonality to the Mean," Statistical Papers, 33, 69-74.
12. Johnson, N. L., and Kotz, S. (1969), Discrete Distributions, New York: Wiley.
13. Jørgensen, B. (1987), "Exponential Dispersion Models," Journal of the Royal Statistical Society, Ser. B, 49, 127-162.
14. _ (1997), The Theory of Dispersion Models, London: Chapman & Hall.
15. Kemp, A. W., and Kemp, C. D. (1966), "An Alternative Derivation of the Hermite Distribution," Biometrika, 53, 627-628.
16. Kemp, C. D., and Kemp, A. W. (1965), "Some Properties of the 'Hermite' Distribution," Biometrika, 52, 381-394.
17. Kokonendji, C. C., Demétrio, C. G. B., and Dossou- Gbété, S. (2004), "Some Discrete Exponential Dispersion Models: Poisson-Tweedie and Hinde-Demétrio Classes," Statistics and Operations Research Transactions, 28, 201-213.
18. Lukacs, E. (1970), Characteristics Functions (2nd ed.), London: Griffin.
19. Mitrinovic, D. S., Pecaric, J. E., and Fink, A. M. (1993), Classical and New Inequalities in Analysis, Dordrecht: Kluwer Academic Publishers.
20. Puig, P. (2003), "Characterizing Additively Closed Discrete Models by a Property of Their MLEs, With an Application to Generalized Hermite Distributions," Journal of the American Statistical Association, 98, 687-692.
21. Rao, C. R., and Chakravarti, I. M. (1956), "Some Small Sample Tests of Significance for a Poisson Distribution," Biometrics, 12, 264-282.
22. Sprott, D. A. (1983), "Estimating the Parameters of a Convolution by Maximum Likelihood," Journal of the American Statistical Association, 78, 457-460.
23. Teicher, H. (1954), "On the Convolution of Distributions," The Annals of Mathematical Statistics, 25, 775-778.
24. _ (1961), "Maximum Likelihood Characterization of Distributions," The Annals of Mathematical Statistics, 32, 1214-1222.
25. Tweedie, M. C. K. (1984), "An Index Which Distinguishes Between Some Important Exponential Families," in Statistics: Applications and New Directions, Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, Calcutta: Indian Statistical Institute, pp. 579-604.
26. van den Broek, J. (1995), "A Score Test for Zero Inflation in a Poisson Distribution," Biometrics, 51, 738-743.
27. Willmot, G. E. (1987), "The Poisson-Inverse Gaussian Distribution as an Alternative to the Negative Binomial," Scandinavian Actuarial Journal, 87, 113-127.