Some applications of probability generating function based methods to statistical estimation

 Access to full text

 Full (PDF)

1. [1] D. Dacunha-Castelle and M. Duflo, Probabilités et Statistiques, Tome 2, Problèmes à temps mobile, Masson, Paris 1983. Zbl0535.62004
2. [2] M.M. Dowling and M. Nakamura, Estimating parameters for discrete distributions via the empirical probability generating function, Commun. Stat., Simulation Comput 26 (1) (1997), 301-313. Zbl0902.62032
3. [3] M.L. Esquível, Probability generating functions for discrete real-valued random variables, Teor. Veroyatn. Primen. 52 (1) (2007), 129-149; translation in Theory Probab. Appl. 52 (1) (2008), 40-57. 
4. [4] M.L. Esquível, Aplicações das funções geradoras de probabilidade a variáveis aleatórias reais, Proceedings of the XII Annual Congress Portuguese Statistical Society, Editors Carlos Braumann, Paulo Infante, Manuela Oliveira, Russell Alpizar Jara e Fernando Rosado (2005), 235-246. 
5. [5] A. Feuerverger, On the empirical saddlepoint approximation, Biometrika 76 (3) (1989), 457-464. Zbl0674.62019
6. [6] A. Feuerverger and P. McDunnough, On statistical transform methods and their efficiency, The Can. J. of Stat. 12 (4) (1984), 303-317. Zbl0566.62021
7. [7] P. Gaenssler, Empirical Processes, Lecture Notes-Monograph Series, volume 3, Institute of Mathematical Statistics, Hayward, CA 1983. 
8. [8] S. Kocherlakota and K. Kocherlakota, Goodness of fit tests for discrete distributions, Commun. Statist.-Theor. Meth. 15 (3) (1986), 815-829. Zbl0618.62049
9. [9] P. Malliavin, Integration and Probability, Springer Verlag 1995. 
10. [10] M.S. Marques and V. Pérez-Abreu, Law of large numbers and central limit theorem for the empirical probability generating function of stationary random sequences and processes, Aportaciones Mat., Notas Invest. 4 (2) (1989), 100-109. Zbl0872.60018
11. [11] M. Nakamura and V. Pérez-Abreu, Empirical probability generating function. An overview, Insur. Math. Econ. 12 (3) (1993), 349-366. Zbl0800.62075
12. [12] M. Nakamura and V. Pérez-Abreu, Exploratory data analysis for counts using the empirical probability generating function, Commun. Stat., Theory Methods 22 (3) (1993), 827-842. Zbl0784.62001
13. [13] M. Nakamura and V. Pérez-Abreu, Use of an empirical probability generating function for testing a Poisson model, Can. J. Stat. 21 (2) (1993), 149-156. Zbl0779.62039
14. [14] W.R. Pestman, Mathematical Statistics, Walter de Gruyter, Paris, New York 1998. Zbl0911.62001
15. [15] B.L.S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Arnold Hodder Headline Group 1999. Zbl0952.62077
16. [16] B. Rémillard and R. Theodorescu, Inference based on the empirical probability generating function for mixtures of Poisson distributions, Stat. Decis. 18 (4) (2000), 349-366. Zbl1179.62046
17. [17] R. Rueda and F. O'Reilly, Tests of fit for discrete distributions based on the probability generating function, Commun. Stat., Simulation Comput. 28 (1) (1999), 259-274. Zbl1054.62546
18. [18] R. Rueda, V. Pérez-Abreu and F. O'Reilly, Goodness of fit for the Poisson distribution based on the probability generating function, Commun. Stat., Theory Methods 20 (10) (1991), 3093-3110. Zbl0800.62093