A Classification of Reproducible Natural Exponential Families in the Broad Sense

Journal of Theoretical Probability

Volumn 16, Issue 1, 2003, Pages 175-196

  Bar Lev, Shaul K ^a   Casalis, Muriel ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Exponential dispersion models; Infinitely divisible distributions; Natural exponential families; Reproducibility; Variance functions

Indexed keywords

EID: 0037273826     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022286606451     Document Type: Article

References (13)

1. Bar-Lev, S. K., and Enis, P. (1986). Reproducibility and natural exponential families with power variance-functions. Ann. Statist. 14, 1507-1522.
2. Barndorff-Nielsen, O. (1978). Information and Exponential Families in Statistical Theory, Wiley, New York.
3. d invariantes par un groupe. J. Stat. Rev. 59, 241-262.
4. Devroye, L. (1986). Non Uniform Random Variate Generation, Springer-Verlag, New York.
5. Jørgensen, B. (1986). Some properties of exponential dispersion models. Scand. J. Statist. 13, 187-198.
6. Jørgensen, B. (1987). Exponential dispersion models (with discussion). J. Roy. Statist. Soc. B,49, 127-162.
7. Jørgensen, B. (1989). Lectures on the Theory of Exponential Dispersion Models and Analysis of Deviance, Monografias de Matematica, Vol. 23, Institute de Mathematica Pura Aplicada, Rio de Janeiro.
8. Jørgensen, B. (1997). The Theory of Dispersion Models, Monographs on Statistics and Applied Probability, Vol. 76, Chapmann and Hall.
9. Letac, G., and Mora, M. (1990). Natural exponential families with cubic variance functions. Ann. Statist. 18, 1-37.
10. Letac, G. (1992). Lectures on Natural Exponential Families and Their Variance Functions, Monografias de Matematica, Vol. 50, Institute de Mathematica Pura Aplicada, Rio de Janeiro.
11. Morris, C. N. (1982). Natural exponential families with quadratic variance functions. Ann. Statist. 10, 65-80.
12. Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families. In Ghosh, J. K., and Roy, J. (eds.), Statistics: Applications and New Directions, Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, Indian Statistical Institute, Calcutta, pp. 579-604.
13. Wilks, S. S. (1963). Mathematical Statistics, Wiley, New York.