Estimation of the Weibull tail-coefficient with linear combination of upper order statistics

Journal of Statistical Planning and Inference

Volumn 138, Issue 5, 2008, Pages 1416-1427

  Gardes, Laurent ^a   Girard, Stéphane ^a  

^a INRIA RHÔNE ALPES   (France)

Author keywords

Extreme values; Order statistics; Regular variations; Weibull tail coefficient

Indexed keywords

EID: 38349053032     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.04.026     Document Type: Article

References (22)

1. Arnold B.C., Balakrishnan N., and Nagaraja H.N. A First Course in Order Statistics (1992), Wiley, New York
2. Bain, L., Engelhardt, M., 1991. Statistical analysis of reliability and life-testing models. Theory and methods, second ed. Statistics: Textbooks and Monographs Series, vol. 115, Marcel Dekker, Inc., New York.
3. Beirlant J., and Teugels J.L. Modeling large claims in non-life insurance. Insurance: Math. Econom. 11 (1992) 17-29
4. Beirlant J., Broniatowski M., Teugels J.L., and Vynckier P. The mean residual life function at great age: applications to tail estimation. J. Statist. Plann. Inference 45 (1995) 21-48
5. Beirlant J., Teugels J., and Vynckier P. Practical Analysis of Extreme Values (1996), Leuven University Press, Leuven
6. Beirlant J., Dierckx G., Goegebeur Y., and Matthys G. Tail index estimation and an exponential regression model. Extremes 2 (1999) 177-200
7. Berred M. Record values and the estimation of the Weibull tail-coefficient. C. R. Acad. Sci. t. Sér. I 312 (1991) 943-946
8. Bingham N.H., Goldie C.M., and Teugels J.L. Regular variation, Encyclopedia of Mathematics and its Applications vol. 27 (1987), Cambridge University Press, Cambridge
9. Broniatowski M. On the estimation of the Weibull tail coefficient. J. Statist. Plann. Inference 35 (1993) 349-366
10. Csörgö S., Deheuvels P., and Mason D. Kernel estimates of the tail index of a distribution. Ann. Statist. 13 (1985) 1050-1077
11. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events (1997), Springer, Berlin
12. Galambos J. The Asymptotic Theory of Extreme Order Statistics (1987), R.E. Krieger Publishing Company, New York
13. Gardes L., and Girard S. Comparison of Weibull tail-coefficient estimators. REVSTAT-Statist. J. 4 (2006) 163-188
14. Geluk, J.L., de Haan, L., 1987. Regular Variation, Extensions and Tauberian Theorems. Math Centre Tracts, vol. 40, Centre for Mathematics and Computer Science, Amsterdam.
15. Girard S. A Hill type estimate of the Weibull tail-coefficient. Commun. Statist. Theory Methods 33 (2004) 205-234
16. Häusler E., and Teugels J.L. On asymptotic normality of Hill's estimator for the exponent of regular variation. Ann. Statist. 13 (1985) 743-756
17. Hill B.M. A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 (1975) 1163-1174
18. Klüppelberg, C., Villaseñor, J.A., 1993. Estimation of distribution tails-a semiparametric approach. Deutschen Gesellschaft für Versicherungsmathematik XXI(2), 213-235.
19. Kratz M., and Resnick S. The QQ-estimator and heavy tails. Stochastic Models 12 (1996) 699-724
20. Mason D.M. Asymptotic normality of linear combinations of order statistics with a smooth score function. Ann. Statist. 9 4 (1981) 899-908
21. Schultze J., and Steinebach J. On least squares estimates of an exponential tail coefficient. Statist. Decisions 14 (1996) 353-372
22. Viharos L. Weighted least-squares estimators of tail indices. Probab. Math. Statist. 19 (1999) 249-265