Extended truncated inverse Gaussian-Poisson model

Statistical Modelling

Volumn 9, Issue 2, 2009, Pages 151-171

  Puig, Xavier ^a   Ginebra, Josep ^a   Perez Casany, Marta ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Distribution of vocabulary; Poisson mixture; Sichel model; Species frequency; Stilometry; Textual data

Indexed keywords

EID: 70449561415     PISSN: 1471082X     EISSN: 14770342     Source Type: Journal    
DOI: 10.1177/1471082X0800900204     Document Type: Article

References (49)

1. Ajiferuke I, Wolfram D and Famoye F (2006) Sample size and informetric model goodness-of-fit outcomes: a search engine log case study. Journal of Information Science, 32, 212-22.
2. Atkinson A and Yeh L (1982) Inference for Sichel's compound Poisson distribution. Journal of the American Statistical Association, 77, 153-58.
3. Baayen H (2001) Word frequency distributions. Dordretch: Kluwer.
4. Böhning D and Kuhnert R (2006) Equivalence of truncated count mixture distributions and mixtures of truncated count distributions. Biometrics, 62, 1207-215.
5. Burrell QL and Fenton MR (1993) Yes, the GIGP really does work-and is workable. Journal of the American Society for Information Science, 44, 61-69.
6. Carlson M (2002) Assessing microdata disclosure risk using the Poisson-inverse Gaussian distribution. Statistics in Transition, 5, 901-25.
7. Chhikara RS and Folks JL (1989) The inverse Gaussian distribution: theory, methodology and applications. New York: Marcel Dekker.
8. Engen S (1974) On species frequency models. Biometrika, 61, 263-70.
9. Giron J, Ginebra J and Riba A (2005) Bayesian analysis of a multinomial sequence and homogeneity of literary style. The American Statistician, 32, 61-74.
10. Good IJ (1953) The population frequencies of species and the estimation of population parameters. Biometrika, 40, 237-64.
11. Griffiths DA (1973) Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total of cases of a disease. Biometrics, 29, 637-48.
12. Heller G (1997) Estimation of the number of classes. South African Statistical Journal, 31, 65-90.
13. Herdan G (1961) A critical examination of Simon's model of certain distribution functions in linguistics. Applied Statistics, 10, 65-76.
14. Herdan G (1964) Quantitative linguistics. London: Butterworth.
15. Holla MS (1966) On a Poisson-inverse Gaussian distribution. Metrika, 11, 115-21.
16. Holmes DI (1992) A stylometric analysis of mormon scripture and related texts. Journal of the Royal Statistical Society Series A, 155, 91-120.
17. Holmes DI and Forsyth RS (1995) The Federalist revisited. New directions in authorship attribution. Literary and Linguistics Computing, 10, 111-27.
18. Hoshino N (2005) Engen's extended negative binomial model revisited. Annals of the Institute of Statistical Mathematics, 57, 369-87.
19. Johnson N and Kotz S (1994) Univariate continuous distributions. New York: John Wiley & Sons.
20. Karlis D (2001) A general EM approach for maximum likelihood estimation in mixed Poisson regression models. Statistical Modelling, 1, 305-18.
21. Klugman SA, Panjer HH and Willmot GE (1998) Loss models. From data to decisions. New York: John Wiley & Sons.
22. Ord JK and Whitmore G (1986) The Poisson-inverse Gaussian distribution as a model for species abundance. Communications in Statistics: Theory and Methods, 15, 853-71.
23. Pollatschek M and Radday YT (1981) Vocabulary richness and concentration in Hebrew biblical literature. Association for Literary and Linguistical Computing Bulletin, 8, 217-31.
24. Riba A (2002) Estadística i Homogeneïtat d'estil al Tirant lo Blanc (in catalan). Unpublished PhD Thesis, Technical University of Catalonia.
25. Riba A and Ginebra J (2006) Diversity of vocabulary and homogeneity of literary style. Journal of Applied Statistics, 33, 729-41.
26. Sankaran M (1968) Mixtures by the inverse Gaussian distribution. Sankhya, Series A, 30, 455-58.
27. Seshadri V (1993) The inverse Gaussian distribution: A case study in exponential families. Oxford: Clarendon Press.
28. Seshadri V (1999) The inverse Gaussian distribution: Statistical theory and applications. New York: Springer Verlag.
29. Sichel HS (1971) On a family of discrete distributions particularly suited to represent long-tailed frequency data. In Proceedings of the third symposium on mathematical statistics. (ed. Laubscher NF), Pretoria: C.S.I.R51-97.
30. Sichel HS (1974) On a distribution representing sentence-length in written prose. Journal of the Royal Statistical Society, Series A, 137, 25-34.
31. Sichel HS (1975) On a distribution law for words frequencies. Journal of the American Statistical Association, 70, 542-47.
32. Sichel HS (1982a) Asymptotic efficiencies of three methods of estimation for the inverse Gaussian-Poisson distribution. Biometrika, 69, 467-72.
33. Sichel HS (1982b) Repeat-buying and the generalized inverse Gaussian-Poisson distribution. Applied Statistics, 31, 193-204.
34. Sichel HS (1985) A bibliometric distribution that really works. Journal of the American Society for Information Science, 36, 314-21.
35. Sichel HS (1986a) Word frequency distributions and type-token characteristics. Mathematical Scientist, 11, 45-72.
36. Sichel HS (1986b) Parameter estimation for a word frequency distribution based on occupancy theory. Communications in Statistics: Theory and Methods15, 935-49.
37. Sichel HS (1992a) Anatomy of the generalized inverse Gaussian-Poisson distribution with special applications to bibliometric studies. Information Processing and Management, 28, 5-17.
38. Sichel HS (1992b) Note on a strongly unimodal bibliometric size frequency distribution. Journal of the American Society for Information Science, 43, 299-303.
39. Shoukri MM, Asyali MH, vanDorp R and Kelton D (2004) The Poisson inverse Gaussian regression model in the analysis of clustered counts data. Journal of Data Science, 2, 17-32.
40. Stein GZ and Juritz JM (1988) Linear models with an inverse Gaussian-Poisson error distribution. Communications in Statistics: Theory and Methods, 17, 557-71.
41. Stein GZ, Zucchini W and Juritz JM (1987) Parameter estimation for the Sichel distribution and its multivariate extension. Journal of the American Statistical Association, 82, 938-44.
42. Tremblay L (1992) Using the Poisson inverse Gaussian in bonus-malus systems. ASTIN Bulletin, 22, 97-106.
43. Willmot GE (1986) Mixed compound Poisson distributions. ASTIN Bulletin, 16, 59-79.
44. Willmot GE (1987) The Poisson-inverse Gaussian distribution as an alternative to the negative binomial. Scandinavian Actuarial Journal, 2, 113-27.
45. Willmot GE (1988a) Parameter orthogonality for a family of discrete distributions. Journal of the American Statistical Association, 83, 517-21.
46. Willmot GE (1988b) A remark on the Poisson Pascal and some other contagious distributions. Statistics and Probability Letters, 7, 217-20.
47. Willmot GE (1988c) Sundt and Jewell's family of discrete distributions. ASTIN Bulletin, 18, 17-29.
48. Yule GU (1944) The statistical study of literary vocabulary. London: Cambridge University Press.
49. Zipf GK (1932) Selected studies of the principle of relative frequency in language. Cambridge: Harvard University Press.