On the power-variance family of probability distributions

Communications in Statistics - Theory and Methods

Volumn 33, Issue 5, 2004, Pages 1007-1029

  Vinogradov, Vladimir ^a  

^a OHIO UNIVERSITY   (United States)

Author keywords

Cumulant; Decomposition criterion; Indecomposable component; Power variance family; Tweedie law; Weak convergence

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; MATHEMATICAL MODELS;

CUMULANT; DECOMPOSITION CRITERION; INDECOMPOSABLE COMPONENT; POWER-VARIANCE FAMILY; TWEEDIE LAW; WEAK CONVERGENCE;

PROBABILITY DISTRIBUTIONS;

EID: 2342614803     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120029821     Document Type: Article

References (24)

1. Bar-Lev, S. K., Enis, P. (1986). Reproducibility and natural exponential families with power variance functions. Ann. Statist. 14:1507-1522.
2. Bertoin, J. (1996). Lévy Processes. Cambridge University Press.
3. Chhikara, R. S., Folks, J. L. (1989). The Inverse Gaussian Distribution. Theory, Methodology, and Applications. New York: Marcel Dekker.
4. Cochran, W. G. (1934). The distribution of quadratic forms in a normal system, with applications to the analysis of covariance. Proc. Camb. Phil. Soc. 30:178-191.
5. Cramér, H. (1970). Random Variables and Probability Distributions. 3rd ed. Cambridge University Press.
6. Dykstra, R. L., Hewett, J. E. (1972). Examples of decompositions of chi-squared variables. Amer. Statist. 26(4):42-43.
7. Hougaard, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika 73:387-396.
8. Hougaard, P. (2000). Analysis of Multivariate Survival Data. New York: Springer.
9. James, G. S. (1952). Notes on a theorem of Cochran. Proc. Camb. Phil. Soc. 48:443-446.
10. Johnson, N. L., Kotz, S., Kemp, A. W. (1992). Discrete Univariate Distributions. 2nd ed. New York: Wiley.
11. Johnson, N. L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions. Vol. 1. 2nd ed. New York: Wiley.
12. Jørgensen, B. (1997). The Theory of Dispersion Models. London: Chapman & Hall.
13. Jørgensen, B., Vinogradov, V. (2002). Convergence to Tweedie models and related topics. In: Balakrishnan, N., ed. Advances on Theoretical and Methodological Aspects of Probability and Statistics. London: Taylor & Francis, pp. 473-489.
14. Küchler, U., Sørensen, M. (1997). Exponential Families of Stochastic Processes. New York: Springer.
15. Linnik, Yu. V. (1964). Decomposition of Probability Distributions. New York: Dover.
16. Linnik, Yu. V., Ostrovskii, I. V. (1977). Decomposition of Random Variables and Vectors. Providence: AMS.
17. Lukacs, E. (1970). Characteristic Functions. 2nd ed. London: Griffin.
18. McCullagh, P., Nelder, J. A. (1989). Generalized Liner Models. 2nd ed. Boca Raton: Chapman & Hall/CRC.
19. Raikov, D. A. (1938). On the decomposition of Gauss' and Poisson's laws. Izvestia Akademii Nauk SSSR. Series A, 91-124 (in Russian).
20. Samorodnitsky, G., Taqqu, M. S. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman & Hall.
21. Teicher, H. (1954). On the factorization of distributions. Ann. Math. Statist. 25:769-774.
22. Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families. In: Ghosh, J. K., Roy, J., eds. Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, Calcutta, Indian Statistical Institute, pp. 579-604.
23. Vinogradov, V. (2002). On a class of Levy processes used to model stock price movements with possible downward jumps. C. R. Math. Rep. Acad. Sci. Canada 24(4): 152-159.
24. Zolotarev, V. M. (1986). One-dimensional Stable Distributions. Providence: AMS.