Domains of attraction for exponential families

Stochastic Processes and their Applications

Volumn 107, Issue 1, 2003, Pages 83-103

  Balkema, August A ^a   Klüppelberg, Claudia ^b   Resnick, Sidney I ^c  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c School of Operations Research and Industrial Engineering   (United States)

Author keywords

Asymptotic normality; Convex conjugate; Domain of attraction; Esscher transform; Exponential family; Gamma distribution; Laplace transform; Normal distribution; Regular variation; Self neglecting; Strongly unimodal

Indexed keywords

EID: 0041340913     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(03)00060-7     Document Type: Article

References (17)

1. Balkema A.A. Klüppelberg C. Resnick S.I. Densities with Gaussian tails Proc. London Math. Soc. 66 1993 568-588
2. Balkema A.A. Klüppelberg C. Stadtmüller U. Tauberian results for densities with Gaussian tails J. London Math. Soc. 51 1995 383-400
3. Balkema A.A. Klüppelberg C. Resnick S.I. Limit laws for exponential families Bernoulli 5 1999 951-968
4. Bar-Lev S.K. Casalis M. Les familles exponentielles naturelles reproduisantes C. R. Acad. Sci. Paris Ser. I Math. 319 1994 1323-1326
5. Bar-Lev S.K. Casalis M. A classification of reproducible natural exponential families in the broad sense J. Theoret. Probability 16 2003 175-196
6. Barndorff-Nielsen O.E. Klüppelberg C. A note on the tail accuracy of the univariate saddlepoint approximation Ann. Toulouse (Sér. 6) 1 1992 5-14
7. Barndorff-Nielsen O.E. Klüppelberg C. Tail exactness of multivariate saddlepoint approximations Scand. J. Statist. 26 1999 1-12
8. Beard R.E. Pentikäinen T. Pesonen R. Risk Theory 3rd Edition 1984 Chapman & Hall London
9. Bingham N.H. Goldie C.M. Teugels J.L. Regular Variation 1987 Cambridge University Press Cambridge, MA
10. Cline D.B.H. Convolution tails, product tails and domains of attraction Probab. Theory Related Fields 72 1986 529-557
11. Daniels H.E. Saddlepoint approximations in statistics Ann. Math. Statist. 25 1954 631-650
12. Embrechts P. Klüppelberg C. Mikosch T. Modelling Extremal Events for Insurance and Finance 1997 Springer Berlin
13. Feigin P. Yashchin E. On a strong Tauberian result Z. Wahrsch. verw. Gebiete 65 1983 35-48
14. Feller, W., 1966. An Introduction to Probability Theory and Its Applications, Vol. II. Wiley, New York.
15. Geluk J.L. de Haan L. Regular Variation, Extensions and Tauberian Theorems 1980 CWI, Mathematisch Centrum Amsterdam
16. Jensen J.L. Uniform saddlepoint approximations Adv. in Appl. Probab. 20 1988 622-634
17. Resnick S.I. Extreme Values, Regular Variation, and Point Processes 1987 Springer New York