Some efficient closed-form estimators of the parameters of the generalized Pareto distribution

Steven G. From1, Suthakaran Ratnasingam2
1University of Nebraska at Omaha
2Department of Mathematics, California State University, San Bernardino, San Bernardino, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Belisle CJP (1992) Convergence theorems for a class of simulated annealing algorithms on Rd. J Appl Probab 29:885–895

Castillo E (1988) Extreme value theory in engineering. Academic Press, New York

Castillo E (1994) Extremes in engineering applications. In: Galambos J et al (ed) Proceedings of the conference on extreme value theory and its applications. Kluwer, Gaithersburg, pp 15–42

Castillo E, Hadi AS (1995a) A method for estimating parameters and quantiles of distributions of continuous random variables. Comput Stat Data Anal 20:421–439

Castillo E, Hadi AS (1995b) Modeling lifetime data with applications to fatigue models. J Am Stat Assoc 90:1041–1054

Castillo E, Hadi AS (1997) Fitting the generalized pareto distribution to data. J Am Stat Assoc 92(440):1609–1620

Cheng S, Chou CH (2000a) On the ABLUE of the scale parameter of the generalized Pareto distribution. Tamakang J Math 31(4):317–330

Cheng S, Chou CH (2000b) On the BLUE of the scale parameter of the generalized Pareto distribution. Tamakang J Math 31(3):165–172

Davison A C (1984) Modelling excesses over high thresholds, with an application. In: Tiago de oliveira J (ed) Statistical extremes and applications, Dordrecht, Reidel, pp 461–482

DuMouchel W (1983) Estimating the stable index $$\sigma $$ in order to measure tail thickness. Ann Stat 11:1019–1036

Galambos J (1981) Extreme value theory in applied probability. Math Sci 6:13–26

Galambos J (1984) Introduction, order statistics, exceedances. law of large numbers. In: Statistical extremes and applications, NATO ASI Series, Dordrecht, Reidel

Grimshaw SD (1993) Computing maximum likelihood estimates for the generalized Pareto distribution. Technometrics 35:185–191

Hosking JRM, Wallis JR (1987) Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29(3):339–349

Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme-value distribution by the method of probability weighted moments. Technometrics 27:251–261

Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3:119–131

Smith R L (1984) Threshold methods for sample extremes. In: Tiago de oliveira J (ed) Statistical extremes and applications, Dordrecht, Reidel, pp 621–638

Smith RL (1985) Maximum likelihood estimation in a class of nonregular cases. Biometrika 72:67–90

Van Montfort MAJ, Witter JV (1986) The generalized pareto distribution applied to rainfall depths. Hydrol Sci J 31:151–162

Walshaw D (1990) Discussion of “models for exceedances over high thresholds. by A. C. Davison and R. L. Smith. J R Stat Soc Ser B 52:393–442