The COM-Poisson model for count data: A survey of methods and applications

Applied Stochastic Models in Business and Industry

Volumn 28, Issue 2, 2012, Pages 104-116

  Sellers, Kimberly F ^a   Borle, Sharad ^b   Shmueli, Galit ^c,d  

^a GEORGETOWN UNIVERSITY   (United States)

^b RICE UNIVERSITY   (United States)

^c UNIVERSITY OF MARYLAND   (United States)

^d INDIAN SCHOOL OF BUSINESS   (India)

Author keywords

biology; Conway Maxwell Poisson; marketing; overdispersion; regression model; transportation; underdispersion

Indexed keywords

APPLIED RESEARCH; BERNOULLI; CONWAY-MAXWELL-POISSON; GEOMETRIC DISTRIBUTION; OVERDISPERSION; REGRESSION MODEL; SPECIAL PROPERTIES; UNDERDISPERSION;

BIOLOGY; DISPERSIONS; MARKETING; REGRESSION ANALYSIS; SURVEYS; TRANSPORTATION;

POISSON DISTRIBUTION;

EID: 84859720220     PISSN: 15241904     EISSN: 15264025     Source Type: Journal    
DOI: 10.1002/asmb.918     Document Type: Article

References (42)

1. von Bortkewicz L,. Das Gesetz der Kleinen Zahlen. Teubner: Leipzig, 1898.
2. Bliss CI, Fisher RA,. Fitting the negative binomial distribution to biological data. Biometrics 1953; 9: 176-199.
3. Etzion H, Pinker E, Seidmann A,. Analyzing the simultaneous use of auctions and posted prices for online selling. Manufacturing and Service Operations Management 2006; 8: 68-91. DOI: 10.1287/msom.1060.0101.
4. McCullagh P, Nelder J,. Generalized Linear Models, 2nd edition. Chapman & Hall/CRC: New York, NY, 1997.
5. Hilbe JM,. Negative Binomial Regression. Cambridge University Press: New York, NY, 2008.
6. Ridout MS, Besbeas P,. An empirical model for underdispersed count data. Statistical Modelling 2004; 4: 77-89. DOI: 10.1191/1471082X04st064oa.
7. del Castillo J, Pérez-Casany M,. Overdispersed and underdispersed Poisson generalizations. Journal of Statistical Planning and Inference 2005; 134: 486-500. DOI: 10.1016/j.jspi.2004.04.019. (Pubitemid 40936096)
8. Consul PC,. Generalized Poisson Distributions: Properties and Applications. Marcel Dekker: New York, NY, 1989.
9. Famoye F,. Restricted generalized Poisson regression model. Communications in Statistics-Theory and Methods 1993; 22: 1335-1354. DOI: 10.1080/03610929308831089.
10. Famoye F, Wang WR,. Censored generalized Poisson regression model. Computational Statistics and Data Analysis 2004; 46: 547-560. DOI: 10.1016/j.csda.2003.08.007. (Pubitemid 38728644)
11. Famoye F,. Statistical control charts for shifted generalized Poisson distribution. Statistical Methods and Applications 2007; 3: 339-354. DOI: 10.1007/BF02589023.
12. Neubauer G, Djuras G,. A generalized Poisson model for underreporting. In Proceedings of the 23rd International Workshop on Statistical Modelling, Eilers PHC, (ed.). Universiteit Utrecht: Netherlands, 2008; 368-373.
13. Pararai M, Famoye F, Lee C,. Generalized Poisson-Poisson mixture model for misreported counts with an application to smoking data. Journal of Data Science 2010; 8: 607-617.
14. Conway RW, Maxwell WL,. A queuing model with state dependent service rates. Journal of Industrial Engineering 1962; 12: 132-136.
15. Shmueli G, Minka TP, Kadane JB, Borle S, Boatwright P,. A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Applied Statistics 2005; 54: 127-142. DOI: 10.1111/j.1467-9876. 2005.00474.x. (Pubitemid 40166926)
16. Guikema SD, Coffelt JP,. A flexible count data regression model for risk analysis. Risk Analysis 2008; 28: 213-223. DOI: 10.1111/j.1539-6924.2008.01014. x. (Pubitemid 351315514)
17. Minka TP, Shmueli G, Kadane JB, Borle S, Boatwright P,. Computing with the COM-Poisson distribution, Technical Report Series, Carnegie Mellon University Department of Statistics, Pennsylvania, 2003
18. Nadarajah S,. Useful moment and CDF formulations for the COM-Poisson distribution. Statistical Papers 2009; 50: 617-622. DOI: 10.1007/s00362-007- 0089-9.
19. Faraway JJ,. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Models. Chapman & Hall / CRC: New York, NY, 2005.
20. Kadane JB, Shmueli G, Minka TP, Borle S, Boatwright P,. Conjugate analysis of the Conway-Maxwell-Poisson distribution. Bayesian Analysis 2005; 1: 363-374. DOI: 10.1214/06-BA113.
21. Rodrigues J, de Castro M, Cancho VG, Balakrishnan N,. COM-Poisson cure rate survival models and an application to a cutaneous melanoma data. Journal of Statistical Planning and Inference 2009; 139: 3605-3611. DOI: 10.1016/j.jspi.2009.04.014.
22. Kokonendji CC, Mizere D, Balakrishnan N,. Connections of the Poisson weight function to overdispersion and underdispersion. Journal of Statistical Planning and Inference 2008; 138: 1287-1296. DOI: 10.1016/j.jspi.2007.05.028.
23. Barron D,. The analysis of count data: overdispersion and autocorrelation. Sociological Methodology 1992; 22: 179-220.
24. Breslow N,. Tests of hypotheses in overdispersed Poisson regression and other quasi-likelihood models. Journal of the American Statistical Association 1990; 85: 565-571.
25. Ismail N, Jemain A,. Handling overdispersion with negative binomial and generalized Poisson regression models. Casualty Actuarial Society Forum, 2007; 103-158.
26. Sellers K, Shmueli G,. A flexible regression model for count data. Annals of Applied Statistics 2010; 4: 943-961. DOI: 10.1214/09-AOAS306.
27. Boatwright P, Borle S, Kadane JB,. A model of the joint distribution of purchase quantity and timing. Journal of the American Statistical Association 2003; 98: 564-572. DOI: 10.1198/016214503000000404. (Pubitemid 37395926)
28. Lord D, Guikema SD, Geedipally SR,. Application of the Conway-Maxwell-Poisson for analyzing motor vehicle crashes. Accident Analysis & Prevention 2008; 40: 1123-1134.
29. Jowaheer V, Khan NAM,. Estimating regression effects in COM-Poisson generalized linear model. World Academy of Science, Engineering and Technology 2009; 53: 1046-1050.
30. Sellers K, Shmueli G,. Data dispersion: Now you see it. now you don't. Robert H. Smith School Research Paper No. RHS 06-122. http://ssrn.com/abstract= 1612755 [21 May 2010].
31. Sellers K, Shmueli G,. A regression model for count data with observation-level dispersion. In In Proceedings of the 24th International Workshop on Statistical Modelling, Booth JG, (ed.). Cornell University: New York, 2009; 337-344.
32. Sellers K, Shmueli G,. Predicting censored count data with COM-Poisson regression. Robert H. Smith School Research Paper No. RHS-06-129. http://ssrn.com/abstract=1702845 [October 29, 2010].
33. Wimmer G, Kohler R, Grotjahn R, Altmann G,. Toward a theory of word length distributions. Journal of Quantitative Linguistics 1994; 1: 98-106. DOI: 10.1080/09296179408590003.
34. Best K-H,. Probability distributions of language entities. Journal of Quantitative Linguistics 2001; 8: 1-11. DOI: 10.1076/jqul.8.1.1.4091.
35. Borle S, Boatwright P, Kadane JB, Nunes J, Shmueli G,. Effect of product assortment changes on consumer retention. Marketing Science 2005; 24: 616-622. DOI: 10.1287/mksc.1050.0121. (Pubitemid 41817691)
36. Kalyanam K, Borle S, Boatwright P,. Deconstructing each item's category contribution. Marketing Science 2007; 26: 327-341. DOI: 10.1287/mksc.1070.0270.
37. Borle S, Dholakia U, Singh S, Westbrook R,. The impact of survey participation on subsequent behavior: an empirical investigation. Marketing Science 2007; 26: 711-726. DOI: 10.1287/mksc.1070.0268.
38. Borle S, Boatwright P, Kadane JB,. The timing of bid placement and extent of multiple bidding: an empirical investigation using ebay online auctions. Statistical Science 2006; 21: 194-205. DOI: 10.1214/088342306000000123. (Pubitemid 44367637)
39. Singh S, Borle S, Jain D,. A generalized framework for estimating customer lifetime value when customer lifetimes are not observed. Quantitative Marketing and Economics 2009; 7: 181-205. DOI: 10.1007/s11129-009-9065-0.
40. Lord D, Geedipally SR, Guikema SD,. Extension of the application of Conway-Maxwell-Poisson models: analyzing traffic crash data exhibiting underdispersion. Risk Analysis 2010; 30: 1268-1276. DOI: 10.1111/j.1539-6924. 2010.01417.x.
41. Kadane JB, Krishnan R, Shmueli G,. A data disclosure policy for count data based on the COM-Poisson distribution. Management Science 2006; 52: 1610-1617. DOI: 10.1287/mnsc.1060.0562. (Pubitemid 44556064)
42. Czado C, Gneiting T, Held L,. Predictive model assessment for count data. Biometrics 2009; 65: 1254-1261. DOI: 10.1111/j.1541-0420.2009.01191.x.